Question 1

Two point charges of +4 μC and -4 μC are separated by a distance of 2 m. What is the magnitude of the electric field at the midpoint between them?

Accepted Answer

At the midpoint, both charges are 1 m away; fields add in the same direction (opposite charges create fields pointing the same way at midpoint), giving E = 2 × (9 × 10⁹ × 4 × 10⁻⁶ / 1²) = 72 × 10³ N/C.

Question 2

Which of the following statements about the Lorentz force on a moving charge is correct?

Accepted Answer

The magnetic force F = q(v × B) is perpendicular to both v and B by the cross-product definition.

Question 3

A parallel plate capacitor has a plate area of 0.5 m² and separation of 2 mm. If the dielectric constant of the medium is 2, calculate the capacitance. (ε₀ = 8.85 × 10⁻¹² F/m)

Accepted Answer

Using C = κε₀A/d = (2 × 8.85 × 10⁻¹² × 0.5)/0.002 = 4.425 × 10⁻⁹ F = 4.425 nF.

Question 4

Two identical point charges repel each other with a force of 8 N when separated by 30 cm. What is the magnitude of each charge? (Take k = 9 × 10⁹ N·m²/C²)

Accepted Answer

From F = kq²/r², we get q² = Fr²/k = (8 × 0.09) / (9 × 10⁹) = 8 × 10⁻¹² , so q = 2√2 × 10⁻⁶ ≈ 4 × 10⁻⁶ C.

Question 5

According to Coulomb's Law, if the distance between two point charges is doubled, the electric force between them becomes:

Accepted Answer

Coulomb's force is inversely proportional to the square of distance (F ∝ 1/r²), so doubling distance makes force one-fourth of original.

Question 6

A proton enters a magnetic field of 0.5 T at an angle of 30° to the field direction with speed 2 × 10⁶ m/s. The magnetic force on the proton is (charge of proton = 1.6 × 10⁻¹⁹ C):

Accepted Answer

F = qvB sin(30°) = 1.6 × 10⁻¹⁹ × 2 × 10⁶ × 0.5 × 0.5 = 8 × 10⁻¹⁴ N.

Question 7

A capacitor of capacitance 10 μF is charged to a potential difference of 100 V. What is the charge stored on the capacitor?

Accepted Answer

Using Q = CV, charge = 10 μF × 100 V = 1000 μC.

Question 8

The electrostatic potential at a distance of 2 m from a point charge of 4 μC in vacuum is approximately:

Accepted Answer

Using V = kQ/r = (9×10⁹ × 4×10⁻⁶)/2 = 18,000 V.

Question 9

The work done in bringing a charge of 5 C from infinity to a point where the electrostatic potential is 200 V is:

Accepted Answer

Work done W = qV = 5 C × 200 V = 1000 J.

Question 10

An electric charge of +2 C is located at the origin. What is the electric field magnitude at a distance of 3 m from this charge?

Accepted Answer

Electric field E = kq/r² = (9 × 10⁹ × 2) / 3² = 18 × 10⁹ / 9 = 2 × 10⁹ N/C.

Question 11

Two capacitors of capacitance 5 μF and 10 μF are connected in series across a 60 V battery. What is the equivalent capacitance?

Accepted Answer

For series connection: 1/C_eq = 1/5 + 1/10 = 3/10, so C_eq = 10/3 ≈ 3.33 μF.

Question 12

A charge of +6 μC is placed in an electric field of magnitude 500 N/C. What is the magnitude of the electric force experienced by the charge?

Accepted Answer

Force F = qE = 6 × 10⁻⁶ × 500 = 3 × 10⁻³ N.

Question 13

A charged particle with charge q = 2 C moves with velocity v = 5 m/s perpendicular to a magnetic field B = 0.4 T. Calculate the magnetic force acting on the particle.

Accepted Answer

Using F = qvB sin(θ), where θ = 90°, F = 2 × 5 × 0.4 × 1 = 4 N.

Question 14

An electron moves in a circular path in a uniform magnetic field. If the magnetic field strength is doubled, what happens to the radius of the circular path?

Accepted Answer

Since r = mv/(qB), radius is inversely proportional to magnetic field; doubling B halves the radius.

Question 15

Two resistors of 6 Ω and 12 Ω are connected in parallel. What is the equivalent resistance?

Accepted Answer

For parallel resistors: 1/R_eq = 1/6 + 1/12 = 3/12 = 1/4, so R_eq = 4 Ω.

Question 16

The SI unit of electrical resistivity is:

Accepted Answer

Resistivity ρ = RA/l, where R is in ohms, A in m², and l in m; thus unit is Ω·m.

Question 17

If the current through a resistor is doubled while keeping resistance constant, how does the power dissipated change?

Accepted Answer

Power P = I²R; if I is doubled, P becomes (2I)²R = 4I²R, which is 4 times the original.

Question 18

A conductor has a length of 2 m, cross-sectional area of 1 mm², and resistivity of 1.6 × 10⁻⁸ Ω·m. Calculate its resistance.

Accepted Answer

R = ρl/A = (1.6 × 10⁻⁸ × 2)/(1 × 10⁻⁶) = 32 Ω.

Question 19

A wire of resistance 10 Ω carries a current of 2 A. What is the potential difference across the wire?

Accepted Answer

Using Ohm's law, V = IR = 2 × 10 = 20 V.

Question 20

A charged particle moves through crossed electric and magnetic fields without deflection. If E = 3 × 10⁵ V/m and B = 0.6 T, calculate the velocity of the particle.

Accepted Answer

For no deflection, electric and magnetic forces balance: qE = qvB, so v = E/B = 3 × 10⁵ / 0.6 = 5 × 10⁵ m/s.

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