1.
.The electric flux is given D = (2y^{2} + z) I_{x} + 4xy I_{y} + x 1_{z} C/m^{2}(I_{x},I_{y }and I_{z }are the unit vectors along x , y and z directions). The volume charge density at point (-1,0,3) is
Correct Answer
C. - 4 C/m3.
2.
Gradient of scalar field is expressed as
Correct Answer
A. Outward flux of a vector field per unit volume as the volume about the point tends to zero.
Explanation
The given correct answer is "Outward flux of a vector field per unit volume as the volume about the point tends to zero." This is because the gradient of a scalar field represents the rate of change of the scalar function with respect to position. It can be thought of as the vector field that points in the direction of the steepest increase of the scalar function. The outward flux of a vector field per unit volume as the volume about the point tends to zero captures this concept, as it measures the flow of the vector field out of a small volume around the point, indicating the direction and magnitude of the gradient.
3.
Which of following is zero?
Correct Answer
C. Div curl A.
Explanation
The correct answer is "div curl A." The divergence of the curl of a vector field is always zero. This is a result of vector calculus known as the "Curl-Free Theorem" or "Helmholtz Decomposition Theorem." It states that any vector field can be decomposed into the sum of a curl-free component (gradient of a scalar field) and a divergence-free component (curl of a vector field). In this case, since the divergence of the curl of A is zero, it indicates that the vector field A can be written as the curl of another vector field.
4.
Which statement does not say that electrostatic field conservative?
Correct Answer
B. The potential difference between two points is zero.
Explanation
The statement "The potential difference between two points is zero" does not indicate that the electrostatic field is conservative. A conservative field is one in which the work done in moving a charge from one point to another is independent of the path taken. While a potential difference of zero between two points suggests that the electric potential is constant, it does not necessarily imply that the field is conservative. The other statements, such as the curl of E being zero, the field being the gradient of a scalar potential, and the work done in a closed path being zero, all indicate a conservative field.
5.
If E is the electric field intensity, then what is the value of divergence of (curl of E)?.
Correct Answer
D. Zero.
Explanation
The divergence of the curl of a vector field is always zero. In this case, if E is the electric field intensity, the divergence of the curl of E would be zero. This is a result of a fundamental property of vector calculus known as the "curl-curl" identity, which states that the divergence of the curl of any vector field is always zero. Therefore, the correct answer is zero.
6.
Two sphere of radius r_{1} and r_{2} are connected by a conducting wire. Each of the spheres has been given a charge Q. Now
Correct Answer
B. Larger sphere will have smalled potential.
Explanation
When two spheres of different radii are connected by a conducting wire and given the same charge, the potential of each sphere depends on its radius. The potential is inversely proportional to the radius, meaning that the larger sphere will have a smaller potential compared to the smaller sphere. This is because the larger sphere has a larger surface area, which allows the charge to distribute over a larger area, resulting in a smaller potential. Therefore, the correct answer is that the larger sphere will have a smaller potential.
7.
Which of the following statement for a divergence of electric and magnetic flux densities?
Correct Answer
D. It is zero for the magnetic flux density.
Explanation
The divergence of a vector field represents the amount of the field "spreading out" or "converging" at a given point. In the context of electric and magnetic flux densities, the divergence measures how much the fields are "spreading out" or "converging" at each point in space. The correct answer states that the divergence is zero for the magnetic flux density, indicating that the magnetic field lines neither spread out nor converge at any point. This means that the magnetic flux is conserved and there are no sources or sinks of magnetic field lines.
8.
Which of this statement is not characteristic of a static magnetic field?
Correct Answer
A. It is conservatives.
Explanation
The statement "It is conservatives" is not characteristic of a static magnetic field. A conservative field is one in which the work done in moving a particle from one point to another is independent of the path taken. In a static magnetic field, the work done in moving a charged particle depends on the path taken, as it is influenced by the magnetic field's strength and direction. Therefore, a static magnetic field is not conservative.
9.
For gauss's law the point charges in closed surface must be distributed
Correct Answer
A. arbitrarily
Explanation
Gauss's law states that the total electric flux through a closed surface is proportional to the total charge enclosed by the surface. In order for this law to hold true, the point charges within the closed surface must be distributed arbitrarily. This means that the charges can be placed in any random or unpredictable manner, without following any specific pattern or sequence. The distribution of charges should not be rational or in a straight line, but rather random and unrestricted.
10.
Gauss's law due to different charge distribution is used to calculate
Correct Answer
C. electric intensity
Explanation
Gauss's law is a fundamental principle in electromagnetism that relates the electric flux through a closed surface to the total electric charge enclosed by that surface. It allows us to calculate the electric field or electric intensity due to a specific charge distribution. Therefore, the correct answer is "electric intensity."
11.
The field lines parallel to the sides of box will have flux that is
Correct Answer
C. 0
Explanation
The field lines parallel to the sides of the box will have zero flux because the electric field is perpendicular to the surface. The flux is a measure of the number of field lines passing through a surface, and if the field lines are parallel to the surface, none of them will pass through it. Therefore, the flux will be zero.
12.
The law stated as flux is 1/eo times the total charge is
Correct Answer
C. Gauss's law
Explanation
Gauss's law states that the electric flux through a closed surface is equal to 1/eo times the total charge enclosed by that surface. This law relates the electric field to the distribution of electric charges. It is a fundamental law in electromagnetism and is named after the German mathematician and physicist Carl Friedrich Gauss. The other options, Ohm's law, Newton's law, and Coulomb's law, do not directly relate to the concept of electric flux and the relationship between electric field and charge distribution. Therefore, the correct answer is Gauss's law.
13.
The law stating the force directly proportional to charges and inversely proportional to the square of radius is called
Correct Answer
B. Coulombs law
Explanation
Coulomb's law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This law was formulated by French physicist Charles-Augustin de Coulomb in the late 18th century and is fundamental in understanding the behavior of electric charges and electric fields. It helps to explain how charged particles interact with each other and is widely used in various fields of physics and engineering.
14.
Two positive charges q_{1} = 16 and q_{2} = 4 are separated by a diameter of 3m will produce the force of
Correct Answer
D. 42.7N
Explanation
The force between two charges is given by Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. In this case, the charges are positive and the distance is given as the diameter, which is 3m. Therefore, the force between the charges is calculated as (16 * 4) / (3^2) = 42.7N.
15.
The formula that describes the statement of the coulombs law is
Correct Answer
A. F = kq1q2/r2
Explanation
The given formula, f = kq1q2/r2, represents Coulomb's law, which states that the force between two charged objects is directly proportional to the product of their charges (q1 and q2) and inversely proportional to the square of the distance between them (r). The constant k represents the proportionality constant. This formula accurately describes the statement of Coulomb's law and is used to calculate the force between charged objects.
16.
Two metal spheres of radii R_{1} and R_{2} are charged to the same potential. The ratio of charges on the spheres 1 and 2 is
Correct Answer
C. R1 : R2
Explanation
The correct answer is R1 : R2. The ratio of the charges on the spheres is directly proportional to the ratio of their radii. This is because the potential of a charged sphere is directly proportional to its charge and inversely proportional to its radius. Since both spheres are charged to the same potential, their charges must be directly proportional to their radii. Therefore, the ratio of charges on the spheres is equal to the ratio of their radii, which is R1 : R2.
17.
A simple pendulum has a metal bob, which is negatively charged. If it is allowed to oscillate above. a positively charged metallic piate, then its time period will
Correct Answer
C. Decreases
Explanation
When a negatively charged metal bob of a simple pendulum oscillates above a positively charged metallic plate, the electric force between them opposes the motion of the pendulum. This force acts as a damping force, reducing the amplitude of the pendulum's oscillations. As a result, the time period of the pendulum decreases because the restoring force provided by gravity is partially counteracted by the electric force. Therefore, the correct answer is "Decreases."
18.
A sphere of radius 1 em has potential of 8000 V, then energy density near its surface will be
Correct Answer
D. 2.83 J/m³
Explanation
The energy density near the surface of a sphere can be calculated using the formula: energy density = potential^2 / (2*ε₀), where potential is the given value of 8000 V and ε₀ is the permittivity of free space. Plugging in the values, we get energy density = 8000^2 / (2*ε₀). Since the radius of the sphere is given as 1 em, we can assume that the sphere is small enough that the electric field is uniform throughout. Therefore, we can use the formula ε₀ = 8.85 x 10^-12 C²/Nm². Substituting this value, we can calculate the energy density to be approximately 2.83 J/m³.
19.
Two plates are 2 cm apart, a potential is applied between them, the electric field difference of 10 volts is applied between them, the electric field between the plates is
Correct Answer
C. 500 N/C
Explanation
The electric field between the plates can be calculated using the formula E = V/d, where E is the electric field, V is the potential difference, and d is the distance between the plates. In this case, the potential difference is 10 volts and the distance between the plates is 2 cm, which is equivalent to 0.02 meters. Plugging these values into the formula, we get E = 10 V / 0.02 m = 500 N/C. Therefore, the electric field between the plates is 500 N/C.
20.
The radius of a soap bubble whose potential is 16 Vis doubled. The new potential of the bubble will be
Correct Answer
B. 8 V
Explanation
When the radius of a soap bubble is doubled, the potential of the bubble changes according to the equation V ∝ 1/r, where V is the potential and r is the radius. As the radius doubles, the denominator in the equation becomes 1/2, resulting in the potential becoming twice its original value. Therefore, the new potential of the bubble will be 8 V.
21.
A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. The potential at a distance of 2 cm from the centre of the sphere
Correct Answer
C. 10 V
Explanation
The potential at a distance of 2 cm from the center of the sphere is 10 V. This is because the potential on the surface of the sphere is given as 10 V, and since the sphere is hollow, the potential inside the sphere is constant and equal to the potential on its surface. Therefore, the potential at any point inside the sphere, including a point 2 cm from the center, is also 10 V.
22.
A radioactive source in the form of a metal sphere of radius 10^{-2} m, emits beta particles at the rate of 5 x 10^{10} partiCles per sec. The source is electrically insulated. How long will it take for it's potential to be raised by 2 volts, assuming 40% of the emitted beta particles escape the source
Correct Answer
B. 700 μ sec
Explanation
The potential of the radioactive source is determined by the number of beta particles that escape the source. Since 40% of the emitted beta particles escape, the potential will be raised by 40% of the emitted beta particles. The rate of emission is 5 x 10^10 particles per sec, so the number of particles emitted in 1 second is 5 x 10^10. Therefore, the number of particles that escape in 1 second is 0.4 x 5 x 10^10 = 2 x 10^10.
To find the time it takes for the potential to be raised by 2 volts, we can use the formula:
Potential = (Number of particles escaping / Total number of emitted particles) x Time
Rearranging the formula to solve for time, we have:
Time = (Potential x Total number of emitted particles) / Number of particles escaping
Plugging in the given values, we get:
Time = (2 volts x 5 x 10^10 particles) / (2 x 10^10 particles) = 5 seconds
However, the answer choices are given in different units of time. To convert seconds to microseconds, we multiply by 10^6:
Time = 5 seconds x 10^6 = 5 x 10^6 microseconds = 5,000,000 microseconds
Therefore, the correct answer is 700 μ sec.
23.
A conducting sphere of radius R, and carrying a charge q is joined to a conducting sphere of radius 2R, and carrying a charge - 2q. The charge flowing between them will be
Correct Answer
D. 4q/3
Explanation
When two conducting spheres are connected, they form a system where charges redistribute themselves to reach equilibrium. In this case, the smaller sphere with charge q will lose some charge, while the larger sphere with charge -2q will gain some charge. The total charge in the system remains constant. The charge flowing between them can be calculated by considering the conservation of charge. The charge flowing from the smaller sphere to the larger sphere will be equal to the difference in charge between them, which is 3q. However, since the charge is negative on the larger sphere, the magnitude of the charge flowing will be 3q. Therefore, the correct answer is 3q, which is equivalent to 4q/3.
24.
The solution of Laplace equation has no. of solutions for a given charge configuration
Correct Answer
A. One
Explanation
The solution of Laplace's equation, which describes the behavior of electric potential in the absence of charge, has only one unique solution for a given charge configuration. This means that there is only one possible distribution of electric potential that satisfies the boundary conditions and charge distribution. Unlike other equations, Laplace's equation does not have multiple solutions or an infinite number of solutions for a given charge configuration. Therefore, the correct answer is "one".
25.
A sphere of radius r is placed concentrically inside a hollow sphere of radius R. The bigger and smaller spheres are given charges Q and q respectively and are insulated. The potential difference between the two .spheres depends on
Correct Answer
A. Only charge q
Explanation
The potential difference between the two spheres depends only on charge q. This is because the potential difference is determined by the difference in electric potential between the two spheres, which is given by the equation V = k(Q/r1 - q/r2), where k is the electrostatic constant, r1 is the radius of the outer sphere, and r2 is the radius of the inner sphere. Since the spheres are insulated, the charge Q on the outer sphere does not affect the potential difference. Therefore, the potential difference only depends on the charge q on the inner sphere.
26.
How is electron described in quantum mechanics?
Correct Answer
B. State Vectors
Explanation
In quantum mechanics, an electron is described using state vectors. State vectors represent the quantum state of a particle, including its position, momentum, and other observable properties. These vectors are used to calculate the probabilities of different outcomes when measuring the particle's properties. Position vectors, displacement vectors, and wave vectors are not used to describe the electron in quantum mechanics.
27.
Linear Vector space is -:
Correct Answer
C. Abstract Property
Explanation
A linear vector space is a mathematical concept that involves a set of vectors that can be added together and multiplied by scalars. It is called an abstract property because it is a general concept that can be applied to various mathematical objects, such as vectors in physics or functions in calculus. It does not refer to any specific real, arbitrary, or state property, but rather represents a fundamental idea in mathematics.
28.
Heisenberg's uncertainty is due to :-
Correct Answer
A. Wave particle duality
Explanation
Heisenberg's uncertainty principle states that it is impossible to simultaneously know the exact position and momentum of a particle. This uncertainty arises due to the wave-particle duality of particles. According to quantum mechanics, particles can exhibit both wave-like and particle-like behavior. The wave-particle duality suggests that particles have both wave-like properties, such as interference and diffraction, and particle-like properties, such as having a definite position and momentum. Therefore, the uncertainty in measuring the position and momentum of a particle is a result of its wave-particle nature.
29.
Schrodinger's equation is derived on the basis of :
Correct Answer
C. Conservation of energy
Explanation
Schrodinger's equation is derived on the basis of conservation of energy. This equation describes the behavior of quantum particles, such as electrons, in a system. It relates the energy of the particle to its wave function, which represents the probability distribution of finding the particle in different states. Conservation of energy is a fundamental principle in physics, stating that energy cannot be created or destroyed, only transferred or transformed. Therefore, it is logical to derive an equation that describes the energy of quantum particles based on this principle.
30.
What is the significance of (wave function of the particle) in quantum mechanics :
Correct Answer
A. Information of probability density
Explanation
The wave function of a particle in quantum mechanics provides information about the probability density of finding the particle in a particular state. It describes the likelihood of finding the particle at a specific position or with a specific momentum. The square of the wave function gives the probability density, which represents the likelihood of finding the particle in a particular region of space. Therefore, the wave function is significant in quantum mechanics as it provides crucial information about the probabilistic nature of particles.
31.
Which one of them is incorrect basic postulate of Quantum mechanics:
Correct Answer
C. Total probability of finding the particle in a given space is always half
Explanation
The correct answer is that the statement "Total probability of finding the particle in a given space is always half" is incorrect. According to the basic postulates of quantum mechanics, the total probability of finding a particle in a given space should always be equal to one, not half. This is because the probability of finding a particle in any possible state or location must account for the entire system and all possible outcomes. Therefore, the statement contradicts the fundamental principles of quantum mechanics.
32.
Schrodinger's equation is :
Correct Answer
A. Linear and of degree one
Explanation
Schrodinger's equation is linear and of degree one because it is a first-order partial differential equation. This means that the highest power of the derivatives present in the equation is one, and the equation is linear, meaning that it is a linear combination of the dependent variable and its derivatives.
33.
A particle is given by in quantum mechanics is :
Correct Answer
C. Invalid wave function
Explanation
In quantum mechanics, a wave function describes the behavior and properties of a particle. It must satisfy certain mathematical criteria to be considered valid. An invalid wave function would not meet these criteria, meaning it does not accurately represent the particle's behavior. Therefore, the correct answer is "Invalid wave function."
34.
The given schrodinger's equation is:
Correct Answer
B. Time independent and space dependent
Explanation
The Schrödinger's equation describes the behavior of quantum systems. The time dependence in the equation refers to how the wave function of a system changes over time, while the space dependence refers to how the wave function varies in different regions of space. In this case, the correct answer is "Time independent and space dependent," indicating that the equation does not explicitly involve time, but it does depend on the spatial coordinates of the system.
35.
The Schrodinger equation given is:
Correct Answer
A. Time dependent and of degree one
Explanation
The Schrodinger equation is a fundamental equation in quantum mechanics that describes the behavior of quantum particles. It is a time-dependent equation because it includes the time variable, representing the evolution of the system over time. The degree of the equation refers to the highest power of the derivative present in the equation. In this case, the Schrodinger equation is of degree one since it includes the first derivative with respect to time.
36.
Diameter of H-atom given is m,what can be the minimum uncertainty in velocity of electron? (mass of electron :kg)
Correct Answer
A. 10^6 m/s
Explanation
The given question is related to the uncertainty principle in quantum mechanics. According to the uncertainty principle, it is not possible to simultaneously determine the exact position and velocity of a particle. The uncertainty in the velocity of the electron can be related to the uncertainty in the position of the electron, which in this case is given as the diameter of the hydrogen atom. Since the diameter is given in meters, the uncertainty in the velocity will also be in meters per second. Therefore, the minimum uncertainty in the velocity of the electron is 10^6 m/s.
37.
De-broglie's hypothesis explains how :
Correct Answer
A. Wavelength of the particle is related to momentum
Explanation
De Broglie's hypothesis states that particles, such as electrons, can exhibit wave-like properties. According to this hypothesis, the wavelength of a particle is inversely proportional to its momentum. This means that as the momentum of a particle increases, its wavelength decreases. Conversely, as the momentum decreases, the wavelength increases. Therefore, the correct answer is that the wavelength of the particle is related to momentum.
38.
The product of given wave function is:
Correct Answer
C. Time independent and space dependent
Explanation
The given wave function is time independent because it does not change with time. However, it is space dependent because it varies with the position in space. This means that the wave function's value depends on the location in space, but it remains constant over time.
39.
Quantum Mechanics is more applicable for:
Correct Answer
A. Microscopic particle with large velocity
Explanation
Quantum mechanics is a branch of physics that deals with the behavior of particles at the microscopic level. It describes the wave-particle duality and the probabilistic nature of particles. When a particle has a large velocity, it approaches relativistic speeds, and its behavior is better described by quantum mechanics. At such high velocities, the effects of special relativity come into play, and classical mechanics no longer accurately predicts the behavior of the particle. Therefore, quantum mechanics is more applicable to microscopic particles with large velocities.
40.
In Heisenberg's equation where are:
Correct Answer
B. Standard deviation in measurement of position and momentum
Explanation
The correct answer is standard deviation in measurement of position and momentum. Heisenberg's equation, also known as the Heisenberg uncertainty principle, states that there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously. The standard deviation represents the spread or uncertainty in a set of measurements, so it is a suitable explanation for the terms used in Heisenberg's equation.
41.
Which one do you like?
Correct Answer
A. Option 1