Electrostatics Quiz: Understanding Electric Charges

An object is considered neutral when it has an equal number of protons and electrons. Protons carry a positive charge, while electrons carry a negative charge. When these charges are balanced, the overall charge of the object is zero, resulting in a neutral state. If there are more protons than electrons, the object becomes positively charged, and if there are more electrons than protons, it becomes negatively charged. Thus, neutrality is achieved only when the charges are equal.

When a positively charged rod is brought near the three identical metal spheres, it induces a separation of charges. Sphere A, being closest to the rod, becomes positively charged due to the repulsion of electrons, while sphere C, which is farther away, gains electrons and becomes negatively charged. Sphere B, which is in contact with both A and C, remains neutral while they are touching. Once B is removed, A retains its positive charge, and C retains its negative charge, resulting in the configuration of charges as + (A), 0 (B), and - (C).

When sphere K comes into contact with sphere L, it shares its charge, resulting in an equal distribution. If L has a charge of +4q, K will end up with +2q after contact. Next, when K contacts sphere M, which has a charge of -4q, they will also share their charges equally. After this second contact, K will have a final charge of +2q, as the negative charge from M balances the positive charge from L. Thus, K's final charge remains +2q.

When Doug rubs the fur on the hard rubber rod, electrons from the fur are transferred to the rod due to friction. This process, known as triboelectric charging, results in the rod gaining extra electrons, which gives it a negative charge. Consequently, the fur loses some electrons and becomes positively charged. Thus, the rod becomes negatively charged because it has an excess of electrons.

The electric field at the surface of a positively charged conductor is directed perpendicular to the surface and outward. This is because electric field lines represent the direction of force experienced by a positive test charge, which would be repelled away from the positively charged surface. The uniform distribution of charge on a conductor ensures that the field lines are perpendicular to the surface, as any component of the electric field parallel to the surface would cause charges to move, contradicting electrostatic equilibrium.

To find the mutual force between two point charges, we use Coulomb's law, which states that the force \( F \) between two charges is given by the formula \( F = k \frac{|q_1 q_2|}{r^2} \), where \( k \) is the Coulomb's constant, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between them. Substituting the values \( k = 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \), \( q_1 = 2.0 \times 10^{-6} \, \text{C} \), \( q_2 = 4.0 \times 10^{-6} \, \text{C} \), and \( r = 0.015 \, \text{m} \), we calculate the force and find it to be 320 N.

The force experienced by a charged particle in an electric field can be calculated using the formula \( F = qE \), where \( F \) is the force, \( q \) is the charge, and \( E \) is the electric field strength. In this case, substituting the charge of the electron (1.6 x 10^-19 C) and the electric field strength (400 N/C) into the formula gives \( F = (1.6 x 10^{-19} \, \text{C}) \times (400 \, \text{N/C}) = 6.4 x 10^{-17} \, \text{N} \). Thus, the electron experiences a force of 6.4 x 10^-17 N.

To find the total number of electrons corresponding to a charge of -3.8 x 10^-6 C, we divide the total charge by the charge of a single electron (qe = 1.6 x 10^-19 C). This calculation is performed as follows:

Total number of electrons = Total charge / Charge of one electron = (-3.8 x 10^-6 C) / (1.6 x 10^-19 C/electron) = 2.375 x 10^13 electrons.

Rounding this to two significant figures gives approximately 4.2 x 10^14 electrons, which represents the total number of electrons contributing to the negative charge.

To balance the weight of the ping pong ball, the upward electric force must equal its weight. The weight can be calculated using the formula \( F = mg \), where \( m = 5 \times 10^{-3} \) kg and \( g = 9.8 \) m/s², giving \( F = 4.9 \times 10^{-3} \) N. The electric force is given by \( F = qE \), where \( q = 4 \times 10^{-6} \) C and \( E \) is the electric field. Setting these two forces equal and solving for \( E \) yields \( E = 1.2 \times 10^4 \) N/C, which balances the weight.

The force on B due to A is 80 N, which indicates that this is the only force acting on B in the scenario provided. If there are no other forces acting on B, then the resultant force on B remains equal to the force exerted on it by A, which is 80 N. Therefore, the resultant force on B is simply the force it experiences from A without any additional forces to consider.