ii) At a point on the equatorial line: Resultant electric field intensity at the point Q is Eg EB sin Q EAE Es cos. e The vectors EA and Ep are acting at an angle 20. EAcos E sin 4TTE (x2 +2 x2 +12 The vectors EA sin and EB sin are opposite to each other and hence cancel out. 4TTEo (x2+2) (x2+ 12 ) The vectors E, cos and EB cos are acting along the same direction and hence add up. x2 +2 )3/2 4TTE x2 +12)3/2
-2 1 4TTED(x212)32 i) Ifi << y, then EaR The direction of electric field intensity at a point on the equatorial line due to a dipole is parallel and opposite to the direction of the dipole moment. If the observation point is far away or when the dipole is very short, then the electric field intensity at a point on the axial line is double the electric field intensity at a point on the equatorial line. i.e. Ifi << x and I << y, then Ep 2 Eo
Torque on an Electric Dipole in a Uniform Electric Field: The forces of magnitude pE act opposite to each other and hence net force acting on the dipole due to external uniform electric field is zero. So, there is no translational motion of the dipole. However the forces are along different lines of action and constitute a couple. Hence the dipole will rotate and experience torque. Torque: Electric Force x distance t q E (2i sin ) = pEsin Case i: If = 0 , then t 0 . Case ii: If 90 , then t- pE (maximum value) Case iii: If -180 , then t- 0. Direction of Torque is perpendicular and into the plane containing p and E. Sl unit of torque is newton metre (Nm).
Work done on an Electric Dipole in Uniform Electric Field: When an electric dipole is placed in a uniform electric field, it experiences torque and tends to allign in such a way to attain stable equilibrium 21 W p E (cos0, cos e2) If Potential Energy is arbitrarily taken zero when the dipole is at 90, then P.E in rotating the dipole and inclining it at an angle is Potential Energy U--p E cos Note: Potential Energy can be taken zero arbitrarily at any position of the dipole. Case i: If e 0 , then U Case ii: If -90 , then U 0 Case iii: If 180 , then U- pE (Unstable Equilibrium) pE (Stable Equilibrium) END