(a) An electric dipole consists of two point charges $q$ and $-q$ separated by a distance $2a$. Derive an expression for the electric field $\vec{E}$ due to this dipole at a point distant $r$ from the centre of the dipole on the equatorial plane. Write the expression for the electric field at a far off point, i.e. $r \gg a$. (b) A dipole is placed in x-y plane such that charges $q$ and $-q$ are located at $x = a$ and $x = b$ respectively. There exists an electric field $\vec{E} = 2 \hat{i} \text{ } \frac{\text{N}}{\text{C}}$ in the region. Calculate the force $\vec{F}$ and torque $\vec{\tau}$ experienced by the dipole.

Year	Paper Code	Set	Position
CBSE 2026	Series 55-1	Set 1	Question 31
CBSE 2026	Series 55-1	Set 2	Question 32
CBSE 2026	Series 55-1	Set 3	Question 33

• Step 1: Stating the fundamental formula / law statement (+1 Mark)
• Step 2: Intermediate mathematical substitution or proof steps (+1 Mark)
• Step 3: Correct final value or conclusion with mandatory SI units (+1 Mark)