Question

1. In the given figure, charge +Q is placed at the centre of a dotted circle. Work done in taking another charge +q from A to B is W1 and from B to C is W2 . Which one of the following is correct: W1 > W2 , W1=W2 and W1 < W2 ?

Answer 1

publish the image bro

Answer 2

Answer:

(i) Now, the dotted line indicate that that the surface is an ‘equipotential surface’, i.e. potential is constant at all points of the surface. So, we can prove that,  

Potential at A= Potential at B= Potential at C

So, VA=VB=VC

Hence, Work done to bring charge from A to B =W1= VA-VB

Work done to bring charge from B to C = W2= VB-VC

So, W1+W2= VA-VB +VB-VC=0

Hence, W1=W2 as VA-VB =VB-VC.

(ii) Consider a permanent dipole of dipole moment →┬P in a uniform external field→┬E. (By permanent dipole, we mean that p exists irrespective of E; it has not been induced by E.) There is a force qE on q and a force –qE on –q. The net force on the dipole is zero, since E is uniform. However, the charges are separated, so the forces act at different points, resulting in a torque on the dipole. When the net force is zero, the torque (couple) is independent of the origin. Its magnitude equals the magnitude of each force multiplied by the arm of the couple (perpendicular distance between the two antiparallel forces).  

Magnitude of torque = q E × 2 a sinθ = 2qaEsinθ.

Its direction is normal to the plane of the paper, coming out of it. The magnitude of →┬P× →┬E is also pEsinθ, and its direction is normal to the paper, coming out of it. Thus,  

τ = →┬P× →┬E