Question 261:
easyThere is an electric field $E$ in x-direction. If the work done in moving a charge of $0.2 \text{ C}$ through a distance of $2 \text{ m}$ along a line making an angle $60^{\circ}$ with x-axis is $4 \text{ J}$, then what is the value of $E$? (1995)
Work done is given by $W = qEd \cos\theta$. Substituting the values: $4 = 0.2 \times E \times 2 \times \cos(60^{\circ})$. This simplifies to $4 = 0.4 \times E \times 0.5$, which gives $E = \frac{4}{0.2} = 20 \text{ N/C}$.
Question 262:
easyCharge $q_2$ is at the centre of a circular path with radius $r$. Work done in carrying charge $q_1$, once around this equipotential path, would be (1994)
A circular path around a point charge is an equipotential surface because the distance $r$ from the central charge $q_2$ is constant. Since the potential difference between any two points on this path is zero, the work done $W = q\Delta V$ is zero.
Question 263:
easyThe angle between the electric lines of force and the equipotential surface is: (2002)
Electric lines of force are always perpendicular to equipotential surfaces. This ensures that the component of the electric field along the equipotential surface is zero, meaning no work is done in moving a charge along it. Thus, the angle is $90^{\circ}$.