Physics - Electrostatics Question with Solution | TestHub
Three point charges +q, -q, and +q are placed at the vertices A, B, and C respectively of an equilateral triangle of side 'a'. Let O be the centroid of the triangle. Match the following quantities with their correct descriptions. (Take )
List - I | List - II |
|---|---|
(P) Electric potential at the centroid O | (1) |
(Q) Magnitude of electric field at the centroid O | (2) |
(R) Magnitude of net force on a charge +Q placed at the midpoint of side BC | (3) |
(S) Torque on an electric dipole placed at the centroid O, aligned parallel to side AB | (4) Non-zero |
Options:
Answer:
Solution:
Let the vertices be A (top), B (bottom-left), C (bottom-right). The distance from each vertex to the centroid O is . P: Electric potential at O is the scalar sum of potentials due to each charge: . So (P)-(1).
Q: Electric field at O requires vector addition. The magnitude of field due to each charge is . By vector addition of fields due to +q at A (along -y), -q at B (towards B), and +q at C (away from C), the net field magnitude is . So (Q)-(2).
R: Let M be the midpoint of BC. The distance from A to M is . The distances from B to M and C to M are . The force on +Q at M due to -q at B and +q at C are equal in magnitude and opposite in direction, so they cancel out. The force due to +q at A is , directed along AM (downwards). Thus, the net force is . So (R)-(3).
S: Torque on an electric dipole . Since the electric field at the centroid O is non-zero (from Q), and the dipole is aligned parallel to side AB, which is not parallel or anti-parallel to the direction of at O, the torque will be non-zero. So (S)-(4).
