Question

The electric field is $100V/m$, at a distance of $20cm$ from the centre of a dielectric sphere of radius $10cm$. Then $E$ at $3cm$ distance from the centre of sphere is:

• A. $100V/m$
• B. $125V/m$
• C. $120V/m$
• D. $zero$

Answer 1

The correct option is C $120V/m$

REF.Image.

Electric field from distance = 100 N/m

R = Radius = 100m

when $(r>R)$

So $E=\frac{K\theta }{r^2}$

$100=\frac{K\theta }{20\times 20\times {10}^{-4}}$

$K\theta =400\times {10}^{-2}...\left(i\right)$

and Electric field from centre distance is 3 cm.

(when $r<R$) $E=\frac{K\theta r}{R^3}$ from (i)equation

$=\frac{400\times {10}^{-2}\times 3\times {10}^{-2}}{10\times 10\times 10\times {10}^{-6}}$

$=\frac{4\times 3\times {10}^{-2}}{{10}^{-3}}=120V/m$

$E=120V/m$