Electrostatics

Question 1

The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant K₁ and K₂ with thickness 3d/8 and d/2, respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If K₁ = 1.25 K₂, the value of K₁ is:

Accepted Answer

2.66. Slabs stacked along the field direction behave as capacitors in series, so C = ε₀A / Σ(tᵢ/Kᵢ), and note the leftover air gap of thickness d/8. Setting this equal to 2ε₀A/d and substituting K₂ = 0.8K₁ gives 1/K₁ = 3/8, so K₁ = 8/3 ≈ 2.66.

Answer

2.33

Answer

1.60

Answer

1.33

Question 2

Two identical charged conducting spheres A and B have their centres separated by a certain distance. Charge on each sphere is q and the force of repulsion between them is F. A third identical uncharged conducting sphere is brought in contact with sphere A first and then with B and finally removed from both. New force of repulsion between spheres A and B (radii of A and B are negligible compared to the distance of separation, so for calculating the force between them they can be considered as point charges) is best given as:

Accepted Answer

3F/8. Identical conductors in contact share their total charge equally. Touching A leaves q/2 on A and q/2 on the third sphere; then touching B shares q/2 + q equally, leaving 3q/4 on B. Coulomb force goes as the product of the charges, so F' = (1/2)(3/4)F = 3F/8.

Answer

3F/5

Answer

2F/3

Answer

F/2

Question 3

An electric dipole with dipole moment 5 x 10⁻⁶ C m is aligned with the direction of a uniform electric field of magnitude 4 x 10⁵ N/C. The dipole is then rotated through an angle of 60° with respect to the electric field. The change in the potential energy of the dipole is:

Accepted Answer

1.0 J. The potential energy of a dipole in a uniform field is U = −pE cos θ, so the change on rotating from 0° to 60° is ΔU = pE(cos 0° − cos 60°) = pE/2. Here pE = 5 x 10⁻⁶ x 4 x 10⁵ = 2 J, giving ΔU = 1.0 J.

Answer

0.8 J

Answer

1.2 J

Answer

1.5 J

Q3.An electric dipole with dipole moment 5 x 10⁻⁶ C m is aligned with the direction of a uniform electric field of magnitude 4 x 10⁵ N/C. The dipole is then rotated through an angle of 60° with respect to the electric field. The change in the potential energy of the dipole is: