Question

Number of electric lines of force from 0.5 C of positive charge in a dielectric medium of dielectric constant 10 is

• A. $5.65\times {10}^9$
• B. $1.13\times {10}^{11}$
• C. $9\times {10}^9$
• D. $8.85\times {10}^{-12}$

Answer 1

The correct option is A $5.65\times {10}^9$

We know that electric field lines comes radially outwards from a positive charge. So, in order to calcuate the total number of electric field lines we need to draw a gaussian surface.
By gauss law we know
$\varphi =\frac{Q}{ϵ}$---(i)
$ϵ={ϵ}_r{ϵ}_0$ ----(ii)
By putting (ii) in (i) we get
$\varphi =\frac{Q}{{ϵ}_r{ϵ}_0}$
$⟹\varphi =\frac{0.5C}{10\times 8.8\times {10}^{-12}}$
$⟹\varphi =5.65\times {10}^{9}N{m}^2/C$