Coulombs Law and Electric Field

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Q1. If the potential difference across a capacitor is doubled, what happens to the stored energy?

Solution:

Energy stored in a capacitor is given by U = 1/2 C V^2. If V is doubled, U becomes 1/2 C (2V)^2 = 2CV^2, which is quadrupled.

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Q2. If two charges of +3 µC and -3 µC are placed 0.2 m apart, what is the magnitude of the force between them?

Solution:

Using Coulomb's law, F = k * |q1 * q2| / r^2 = (8.99 x 10^9 N m²/C²) * |3 x 10^-6 C * -3 x 10^-6 C| / (0.2 m)^2 = 45 N.

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Q3. In a parallel circuit with a total voltage of 12 V, what is the voltage across each resistor?

Solution:

In a parallel circuit, the voltage across each resistor is equal to the total voltage, so it is 12 V.

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Q4. What is the electric field strength at a distance of 2 m from a charge of +5 µC?

Solution:

E = k * |q| / r^2 = (8.99 x 10^9 N m²/C²) * |5 x 10^-6 C| / (2 m)^2 = 1.125 N/C.

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Q5. A capacitor of 10 µF is charged to a voltage of 5 V. What is the energy stored in the capacitor?

Solution:

Energy stored, U = 0.5 * C * V² = 0.5 * 10 x 10^-6 F * (5 V)² = 0.125 mJ.

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Q6. In a parallel circuit with a 12 V battery and two resistors of 4 Ω and 6 Ω, what is the total current supplied by the battery?

Solution:

Total resistance, R_eq = 1/(1/4 + 1/6) = 2.4 Ω. Total current, I = V/R_eq = 12 V / 2.4 Ω = 5 A.

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Q7. If the electric potential at a point is 100 V and the charge at that point is 2 µC, what is the electric potential energy?

Solution:

Potential energy U = V * q = 100 V * 2 x 10^-6 C = 0.0002 J = 0.2 J.

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Q8. What is the equivalent resistance of three 4 Ω resistors in series?

Solution:

R_eq = R1 + R2 + R3 = 4 Ω + 4 Ω + 4 Ω = 12 Ω.

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Q9. What is the capacitance of a capacitor that stores 20 µC of charge at a potential difference of 5 V?

Solution:

C = Q/V = 20 x 10^-6 C / 5 V = 4 µF.

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Q10. Two charges, +4 µC and -4 µC, are placed 1 m apart. What is the net electric field at the midpoint between the charges?

Solution:

The electric fields due to both charges at the midpoint are equal in magnitude and opposite in direction, resulting in a net electric field of 0 N/C.