Coulombs Law and Electric Field - Capacitance and Dielectrics

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Q1. What is the energy stored in a capacitor of 5 µF charged to a voltage of 10 V?

Solution:

Energy (U) = 0.5 * C * V² = 0.5 * 5 x 10^-6 F * (10 V)² = 0.25 mJ.

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Q2. What is the voltage across a 10 Ω resistor carrying a current of 2 A?

Solution:

Using Ohm's law, V = I * R = 2 A * 10 Ω = 20 V.

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Q3. What is the capacitance of a parallel plate capacitor with an area of 0.01 m² and a separation of 0.001 m, filled with a dielectric of k=2?

Solution:

C = k * ε₀ * (A/d) = 2 * (8.85 x 10^-12 F/m) * (0.01 m² / 0.001 m) = 4.4 µF.

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Q4. What is the potential difference across a 5 µF capacitor charged to 10 V?

Solution:

Energy stored in a capacitor, U = 0.5 * C * V^2 = 0.5 * (5 x 10^-6 F) * (10 V)^2 = 0.05 J.

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Q5. What is the force between two point charges of +2 µC and -3 µC separated by a distance of 0.5 m?

Solution:

Using Coulomb's law, F = k * |q1 * q2| / r^2 = (8.99 x 10^9 N m²/C²) * |(2 x 10^-6 C) * (-3 x 10^-6 C)| / (0.5 m)^2 = 0.24 N.

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Q6. What is the capacitance of a capacitor with a charge of 6 µC and a voltage of 12 V?

Solution:

C = Q/V = 6 x 10^-6 C / 12 V = 0.5 x 10^-6 F = 0.5 µF.

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Q7. What is the force on a charge of +1 µC placed in an electric field of 1000 N/C?

Solution:

F = q * E = (1 x 10^-6 C) * (1000 N/C) = 0.001 N.

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Q8. If a capacitor of 10 µF is connected in series with a 20 µF capacitor, what is the total capacitance?

Solution:

1/C_total = 1/C1 + 1/C2 = 1/10 + 1/20 = 3/20, thus C_total = 20/3 µF = 6.67 µF.

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Q9. What is the force between two charges of +1 µC and +1 µC separated by 1 m?

Solution:

F = k * |q1 * q2| / r^2 = (8.99 x 10^9 N m²/C²) * (1 x 10^-6 C)² / (1 m)² = 8.99 N.

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Q10. What is the electric potential at a point 3 m away from a charge of +1 µC?

Solution:

V = k * q / r = (8.99 x 10^9 N m²/C²) * (1 x 10^-6 C) / 3 m = 3000 V.