(a) An electric dipole of dipole moment \overrightarrow{p} is placed in a uniform electric field \overrightarrow{E} at an angle \theta with it. Derive the expression for torque ( \overrightarrow{\tau } ) acting on it. Find the orientation of the dipole relative to the electric field for which torque on it is (i) maximum, and (ii) half of maximum.

(b) Two point charges q_{1}+1 \mu C and q_{2}+4 \mu C are placed 2 m apart in air. At what distance from q1 along the line joining the two charges, will the net electric field be zero ?

 

 

 
 
 
 
 

Answers (1)
S safeer

a) Let us consider, the force on either charge be ;-

F=qE

we know, the magnitude of torque is given as ;

\tau = either force \times perpendicular distance between them

therefore,

\tau =qE\; 2a\; \sin \theta  

Such that, p=2qa (From the definition of dipole moment)

 \tau =PE\sin \theta

\tau =p\times E

i) i) for maximum Torque, dipole should be placed perpendicular to the direction of the electric field

ii) For half of the torque

\theta=30^0

b)

Let x be the distance from q_1 where electric field =0

Then the distance from q_2 is 2-x

\\E_1\ and \ E_2 \ are \ opposite \ in\ direction\\E_1-E_2=0\\E_1=E_2\\\frac{k\times1\mu C}{x^2}=\frac{k\times2\mu C}{(2-x)^2}\\\\2-x=2x\\x=\frac{2}{3}m

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