Moving Charges And Magnetism

1. To convert a galvanometer into an ammeter, we connect

Low resistance in series

Low resistance in parallel

High resistance in series

High resistance in parallel

To convert a galvanometer into an ammeter, we connect a low resistance in parallel. This is because an ammeter is used to measure current, and it needs to have a very low resistance in order to minimize the voltage drop across it and ensure accurate current measurement. By connecting a low resistance in parallel with the galvanometer, we provide an alternative path for current to flow, bypassing most of it away from the galvanometer coil. This allows the majority of the current to pass through the low resistance, resulting in a small voltage drop and accurate current measurement on the ammeter.

Explanation

To convert a galvanometer into an ammeter, we connect a low resistance in parallel. This is because an ammeter is used to measure current, and it needs to have a very low resistance in order to minimize the voltage drop across it and ensure accurate current measurement. By connecting a low resistance in parallel with the galvanometer, we provide an alternative path for current to flow, bypassing most of it away from the galvanometer coil. This allows the majority of the current to pass through the low resistance, resulting in a small voltage drop and accurate current measurement on the ammeter.

2. When a charged particle enters in a uniform magnetic field, its kinetic energy

Remains constant

Increases

Decreases

Becomes zero

When a charged particle enters a uniform magnetic field, its kinetic energy remains constant. This is because the magnetic field does not exert any force on the charged particle in the direction of its motion. As a result, the particle's speed and hence its kinetic energy remain unchanged. The magnetic field only acts perpendicular to the particle's velocity, causing it to move in a circular path but not affecting its kinetic energy.

Explanation

When a charged particle enters a uniform magnetic field, its kinetic energy remains constant. This is because the magnetic field does not exert any force on the charged particle in the direction of its motion. As a result, the particle's speed and hence its kinetic energy remain unchanged. The magnetic field only acts perpendicular to the particle's velocity, causing it to move in a circular path but not affecting its kinetic energy.

3. Currents of 10 ampere and 2 ampere are passed through two parallel wires A and B respectively in opposite directions. If the wire A is infinitely long and the length of the wire B is 2m. The force acting on the conductor B, which is situated at 10 cm distance form A will be

8 X 10–5N

5 X 10–5N

8π X 10–7N

4π X 10–7N

When two parallel wires carry currents in opposite directions, they create a magnetic field that interacts with each other. The force between the wires can be calculated using the formula F = (μ₀ * I₁ * I₂ * L) / (2 * π * r), where F is the force, μ₀ is the permeability of free space, I₁ and I₂ are the currents in the wires, L is the length of wire B, and r is the distance between the wires. In this case, since wire A is infinitely long, we can assume that the force acting on wire B is solely due to the magnetic field created by wire A. Therefore, the force acting on wire B will be 8 X 10⁻⁵N.

Explanation

When two parallel wires carry currents in opposite directions, they create a magnetic field that interacts with each other. The force between the wires can be calculated using the formula F = (μ₀ * I₁ * I₂ * L) / (2 * π * r), where F is the force, μ₀ is the permeability of free space, I₁ and I₂ are the currents in the wires, L is the length of wire B, and r is the distance between the wires. In this case, since wire A is infinitely long, we can assume that the force acting on wire B is solely due to the magnetic field created by wire A. Therefore, the force acting on wire B will be 8 X 10⁻⁵N.

4. A wire is placed parallel to the lines of force in mangnetic field and current flows in the wire. Then

The wire will experience a torque

The wire will experience a force along the direction of magnetic field

The wire will not experience any force

The wire will experience a perpendicular force.

When a wire is placed parallel to the lines of force in a magnetic field and current flows through it, the wire will not experience any force. This is because the magnetic force on a current-carrying wire is given by the equation F = BILsinθ, where B is the magnetic field strength, I is the current, L is the length of the wire, and θ is the angle between the wire and the magnetic field. When the wire is parallel to the magnetic field lines, the angle θ is 0, resulting in sinθ = 0. Therefore, the force on the wire is zero and it does not experience any force.

Explanation

When a wire is placed parallel to the lines of force in a magnetic field and current flows through it, the wire will not experience any force. This is because the magnetic force on a current-carrying wire is given by the equation F = BILsinθ, where B is the magnetic field strength, I is the current, L is the length of the wire, and θ is the angle between the wire and the magnetic field. When the wire is parallel to the magnetic field lines, the angle θ is 0, resulting in sinθ = 0. Therefore, the force on the wire is zero and it does not experience any force.

5. A circular coil of radius 4 cm and 20 turns carries a current of 3A. It is placed in a magnetic field of induction 0.5T. The magnetic dipole moment of the coil is

0.6Am2

0.45 Am2

0.3 Am2

0.15 Am2

The magnetic dipole moment of a coil is given by the formula M = nIA, where n is the number of turns, I is the current, and A is the area of the coil. In this case, the number of turns is 20, the current is 3A, and the radius of the coil is 4 cm. The area of the coil can be calculated using the formula A = πr^2. Plugging in the values, we get A = π(0.04m)^2 = 0.005 m^2. Substituting all the values into the formula for the magnetic dipole moment, we get M = 20 * 3A * 0.005 m^2 = 0.3 Am^2. Therefore, the correct answer is 0.3 Am2.

Explanation

The magnetic dipole moment of a coil is given by the formula M = nIA, where n is the number of turns, I is the current, and A is the area of the coil. In this case, the number of turns is 20, the current is 3A, and the radius of the coil is 4 cm. The area of the coil can be calculated using the formula A = πr^2. Plugging in the values, we get A = π(0.04m)^2 = 0.005 m^2. Substituting all the values into the formula for the magnetic dipole moment, we get M = 20 * 3A * 0.005 m^2 = 0.3 Am^2. Therefore, the correct answer is 0.3 Am2.

6. If a particle is moving in a uniform magnetic field, then

Its momentum changes but total energy ramains the same

Both momentum and total energy remains the same

Its total energy changes but momentum remains same

Both momentum and tatal energy will change

When a particle is moving in a uniform magnetic field, its momentum changes due to the Lorentz force acting on it. However, the total energy of the particle remains the same. This is because the magnetic force only affects the particle's motion perpendicular to the magnetic field, causing it to move in a circular path. As a result, the particle's kinetic energy may change, but its total energy (which includes both kinetic and potential energy) remains constant.

Explanation

When a particle is moving in a uniform magnetic field, its momentum changes due to the Lorentz force acting on it. However, the total energy of the particle remains the same. This is because the magnetic force only affects the particle's motion perpendicular to the magnetic field, causing it to move in a circular path. As a result, the particle's kinetic energy may change, but its total energy (which includes both kinetic and potential energy) remains constant.

7. Two parallel conductors are carrying current 'i' in the same direction. Force experienced per unit length by each conductor (distance between the conductors is r) would be

Repulsion and

Attraction and

When two parallel conductors are carrying current in the same direction, they create magnetic fields around them that interact with each other. According to the right-hand rule, the magnetic field lines produced by one conductor will be in the opposite direction to the magnetic field lines produced by the other conductor. This results in an attraction force between the two conductors. Therefore, the correct answer is "Attraction and".

Explanation

When two parallel conductors are carrying current in the same direction, they create magnetic fields around them that interact with each other. According to the right-hand rule, the magnetic field lines produced by one conductor will be in the opposite direction to the magnetic field lines produced by the other conductor. This results in an attraction force between the two conductors. Therefore, the correct answer is "Attraction and".

8. A particle A has charge + q and a particle B has charge + 4q with each of them having the same mass m. When allowed to fall from rest through the same electric potential difference, the ratio of their speeds u_A/ u_{B will therefore:}

2 : 1

1 : 2

1 : 4

4 : 1

When particles A and B are allowed to fall through the same electric potential difference, the ratio of their speeds can be determined using the equation for the electric potential energy gained by a charged particle. The electric potential energy gained by particle A is qV, where V is the electric potential difference, and the electric potential energy gained by particle B is 4qV. Since both particles have the same mass, the kinetic energy gained by each particle is equal to their respective electric potential energies. Therefore, the ratio of their speeds is equal to the square root of the ratio of their electric potential energies, which is equal to the square root of (qV) / (4qV), or 1/2. Thus, the ratio of their speeds is 1 : 2.

Explanation

When particles A and B are allowed to fall through the same electric potential difference, the ratio of their speeds can be determined using the equation for the electric potential energy gained by a charged particle. The electric potential energy gained by particle A is qV, where V is the electric potential difference, and the electric potential energy gained by particle B is 4qV. Since both particles have the same mass, the kinetic energy gained by each particle is equal to their respective electric potential energies. Therefore, the ratio of their speeds is equal to the square root of the ratio of their electric potential energies, which is equal to the square root of (qV) / (4qV), or 1/2. Thus, the ratio of their speeds is 1 : 2.

9. An electron is moving along the positive X-axis. You want to apply a magnetic field for a short times so that the electron may reverse its direction and move parallel to the negative X-axis. This can be done by applying the magnetic field along

X-axis only

Y-axis only

Z-axis only

Y and Z axes

To reverse the direction of the electron and make it move parallel to the negative X-axis, a magnetic field needs to be applied perpendicular to the current direction of the electron. Since the electron is moving along the positive X-axis, the magnetic field should be applied along the Y and Z axes, which are perpendicular to the X-axis. This will exert a force on the electron in a direction opposite to its velocity, causing it to reverse its direction and move parallel to the negative X-axis.

Explanation

To reverse the direction of the electron and make it move parallel to the negative X-axis, a magnetic field needs to be applied perpendicular to the current direction of the electron. Since the electron is moving along the positive X-axis, the magnetic field should be applied along the Y and Z axes, which are perpendicular to the X-axis. This will exert a force on the electron in a direction opposite to its velocity, causing it to reverse its direction and move parallel to the negative X-axis.

10. Two insulating rings, one of slightly smaller diameter than the other are suspended along their common diameter as shown. Initially the planes of the rings are mutually perpendicular. When a steady current is set up in each of them

The two rings rotate into a common plane

The inner ring oscillates about its initial position

The inner ring stays stationary while the outer one moves into the plane of the inner ring

The outer ring stays stationary while the inner one moves into the plane of the outer ring

When a steady current is set up in each of the rings, a magnetic field is produced around each ring. These magnetic fields interact with each other, causing a torque on the rings. The torque causes the rings to rotate, aligning themselves into a common plane. This is because the interaction between the magnetic fields tends to minimize the energy of the system, and aligning the rings into a common plane achieves this. Therefore, the correct answer is that the two rings rotate into a common plane.

Explanation

When a steady current is set up in each of the rings, a magnetic field is produced around each ring. These magnetic fields interact with each other, causing a torque on the rings. The torque causes the rings to rotate, aligning themselves into a common plane. This is because the interaction between the magnetic fields tends to minimize the energy of the system, and aligning the rings into a common plane achieves this. Therefore, the correct answer is that the two rings rotate into a common plane.

11. E, F and G are three current carrying linear conductors. The direction of net magnetic force on F will be

In the direction of current flowing in F

In the plane of paper towards left

In the plane of paper towards right

Normal to the plane of paper

The direction of the net magnetic force on F will be in the plane of the paper towards the left because when current flows through a conductor, a magnetic field is created around it. According to the right-hand rule, the direction of the magnetic field around a current-carrying conductor is in a circular pattern perpendicular to the direction of the current. Since F is a current-carrying conductor, the magnetic field created by it will be in the plane of the paper. The force on F will be perpendicular to both the magnetic field and the current direction, resulting in a net force towards the left.

Explanation

The direction of the net magnetic force on F will be in the plane of the paper towards the left because when current flows through a conductor, a magnetic field is created around it. According to the right-hand rule, the direction of the magnetic field around a current-carrying conductor is in a circular pattern perpendicular to the direction of the current. Since F is a current-carrying conductor, the magnetic field created by it will be in the plane of the paper. The force on F will be perpendicular to both the magnetic field and the current direction, resulting in a net force towards the left.

12. A proton moving with a constant velocity passes through a region of space without change in its velocity. If E and B represent electric and magnetic fields respectively, this region of space may not have

E ≠ 0, B = 0

E ≠ 0, B ≠ 0

E = 0, B ≠ 0

E = 0, B = 0

In this scenario, the proton is moving with a constant velocity, which means that it is not experiencing any acceleration. According to the Lorentz force equation, the force on a charged particle is given by F = q(E + v x B), where q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field. Since the proton is not experiencing any acceleration, the net force on it must be zero. This implies that either the electric field (E) or the magnetic field (B) must be zero. Since the proton is not experiencing any change in velocity, it cannot be influenced by an electric field (E ≠ 0), but it can still pass through a region with zero magnetic field (B = 0). Therefore, the correct answer is E ≠ 0, B = 0.

Explanation

In this scenario, the proton is moving with a constant velocity, which means that it is not experiencing any acceleration. According to the Lorentz force equation, the force on a charged particle is given by F = q(E + v x B), where q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field. Since the proton is not experiencing any acceleration, the net force on it must be zero. This implies that either the electric field (E) or the magnetic field (B) must be zero. Since the proton is not experiencing any change in velocity, it cannot be influenced by an electric field (E ≠ 0), but it can still pass through a region with zero magnetic field (B = 0). Therefore, the correct answer is E ≠ 0, B = 0.

13. Two identical magnetic dipoles of magnetic moment 1.0 A m² each, placed at a separation of 2 m with their axes perpendicular to each other. The resultant magnetic field at a point midway between the dipoles is

T

The resultant magnetic field at a point midway between the dipoles is zero. This is because the magnetic fields produced by the two dipoles cancel each other out due to their perpendicular alignment. The magnetic field produced by one dipole will have equal magnitude but opposite direction to the magnetic field produced by the other dipole. As a result, the net magnetic field at the midpoint will be zero.

Explanation

The resultant magnetic field at a point midway between the dipoles is zero. This is because the magnetic fields produced by the two dipoles cancel each other out due to their perpendicular alignment. The magnetic field produced by one dipole will have equal magnitude but opposite direction to the magnetic field produced by the other dipole. As a result, the net magnetic field at the midpoint will be zero.

14. A galvanometer of resistance 100 Ω gives full scale deflection for 20 mV. Find the resistance to be attached so that it gives full scale deflection of 5V.

In parallel

In Series

In parallel

In Series

To achieve a full scale deflection of 5V on the galvanometer, a resistance needs to be attached in series with it. This is because when resistances are connected in series, the total resistance increases. By increasing the total resistance, the current passing through the galvanometer decreases, resulting in a larger voltage drop across it. Therefore, connecting the resistance in series will allow the galvanometer to give a full scale deflection of 5V.

Explanation

To achieve a full scale deflection of 5V on the galvanometer, a resistance needs to be attached in series with it. This is because when resistances are connected in series, the total resistance increases. By increasing the total resistance, the current passing through the galvanometer decreases, resulting in a larger voltage drop across it. Therefore, connecting the resistance in series will allow the galvanometer to give a full scale deflection of 5V.

15. A bar magnet has a magnetic moment

, and is placed in a magnetic field of 0.2 T. work done in turning the magnet from parallel to anti parallel position relative to the field direction is

0.5 J

1 J

2.0 J

Zero

When a bar magnet is turned from parallel to antiparallel position relative to the magnetic field, work is done against the magnetic field. The work done is given by the formula W = -magnetic moment x change in angle, where the negative sign indicates work done against the field. In this case, the change in angle is 180 degrees, and the magnetic moment is given. Plugging in the values, we get W = -magnetic moment x change in angle = -magnetic moment x 180 degrees. Since the magnetic moment is positive and the change in angle is 180 degrees, the work done is negative. Therefore, the correct answer is Zero.

Explanation

When a bar magnet is turned from parallel to antiparallel position relative to the magnetic field, work is done against the magnetic field. The work done is given by the formula W = -magnetic moment x change in angle, where the negative sign indicates work done against the field. In this case, the change in angle is 180 degrees, and the magnetic moment is given. Plugging in the values, we get W = -magnetic moment x change in angle = -magnetic moment x 180 degrees. Since the magnetic moment is positive and the change in angle is 180 degrees, the work done is negative. Therefore, the correct answer is Zero.