Question 221: Electrostatics & Capacitance

Question

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density $\sigma_{\mathrm{o}}$. Choose the correct option from the following.

Accepted Answer

We know, electric field due to uniformly charged infinite plane sheet,
$$E = {{{\sigma _0}} \over {2{\varepsilon _0}}}$$
perpendicularly directed away from the sheet for positive charge
So, $$\overrightarrow E  = {{{\sigma _0}} \over {2{\varepsilon _0}}} \uparrow 	heta $$
note : E is constant
Let length of dipole = d
so dipole moment, $$\overrightarrow p  = qd \uparrow $$
We know,
Torque, $$\overrightarrow 	au   = \overrightarrow p  	imes \overrightarrow E $$
$$\overrightarrow 	au   = qd\widehat i 	imes {{{\sigma _0}} \over {2{\varepsilon _0}}}\widehat i$$
$$\widehat 	au  = O$$ (as $$\widehat i 	imes \widehat i = 0$$)
force, on charge $$ - q,\overrightarrow {{F_1}}  =  - qE\widehat i$$
on charge $$ + q,\overrightarrow {{F_2}}  = qE\widehat i$$
So net force on dipole, $$\overrightarrow F  = \overrightarrow {{F_1}}  + \overrightarrow {{F_2}} $$
$$ =  - qE\widehat i + qE\widehat i$$
$$\overrightarrow F  = O$$
We know, potential energy of dipole
$$u(O) =  - pE\cos 	heta $$
here, $$O = 0^\circ $$ (given)
So, $${u_{\min }} =  - pE$$
Hence, option B is correct.

Answer

Torque on dipole is zero and net force is directed away from the sheet.

Answer

Potential energy of dipole is minimum and torque is zero.

Answer

Potential energy and torque both are maximum.

Answer

Torque on dipole is zero and net force acts towards the sheet.

Electrostatics & Capacitance

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density \sigma_{\mathrm{o}}. Choose the correct option from the following.

Choose the correct answer: