Question

( vec{E} ) due for ring along its axis
[
E(x)=frac{(2 x)}{left(x^{2}+R^{2}right)^{3 / 2}}
]
forer on the dipole ( , F=D frac{d E}{d x} )
[
begin{aligned}
frac{d E}{d x} &=k Qleft[frac{left(x^{2}+R^{2}right)^{3 / 2}-3left(2-left(x^{2}+R^{2}right)^{1 / 2}right.}{left(x^{2}+R^{2}right)^{3}} cdot 2 x cdot xright]
&=k Q sqrt{x^{2}+R^{2}} cdotleft[frac{x^{2}+R^{2}-3 x^{2}}{left(x^{2}+R^{2}right)^{3}}right]
&=operatorname{KQ} sqrt{x^{2}+R^{2}}left[frac{R^{2}-2 x^{2}}{left(x^{2}+R^{2}right)^{3}}right]
A t x=& R / sqrt{2}, quad frac{d E}{d x}=0
end{aligned}
]
( 80, ) force on dipole ( , F=0 )

# V2R (C) 9R Q.63 (D) 29R TT TT An electric dipole is kept on the axis of a uniformly charged ring at distance R ring. The direction of the dipole moment is along the axis. The dipole moment is P, charge of the ring is Q and 2 from the centre of the radius of the ring is R. The force on the dipole is nearly 4kPO 4KPQ 2kPO (A) 3J3R? (B) 3 3R3 (C) 3J3R (D) zero Q.64 A large sheet carries uniform surface charge density o. Arod of length 21

Solution