CBSE Class 12 · 2014 · ElectrostaticsLong Answer

(a) Deduce the expression for the torque acting on a dipole of dipole moment

p

in the presence of a uniform electric field

E

. (b) Consider two hollow concentric spheres,

S_{1}

and

S_{2}

, enclosing charges

2 Q

and

4 Q

respectively as shown in the figure. (i) Find out the ratio of the electric flux through them. (ii) How will the electric flux through the sphere

S_{1}

change if a medium of dielectric constant

ε_{r}

is introduced in the space inside

S_{1}

in place of air? Deduce the necessary expression.

Solution

(a) The forces

+ q E

and

- q E

form a couple of arm

2 a sin θ

τ = (q E) (2 a sin θ) = pE sin θ, τ = p \times E

(b)(i)

S_{1}

encloses

2 Q

;

S_{2}

encloses

2 Q + 4 Q = 6 Q

ϕ_{S_{1}} = \frac{2 Q}{ε _{0}}, ϕ_{S_{2}} = \frac{6 Q}{ε _{0}}

\frac{ϕ _{S_{1}}}{ϕ _{S_{2}}} = \frac{1}{3}

(ii) With a medium of dielectric constant

ε_{r}

inside

S_{1}

ϕ_{S_{1}} = \frac{2 Q}{ε _{0} ε _{r}}

so the flux is reduced by the factor

ε_{r}

CBSE Class 12 Board · 2014 · Subjective