Question

charge a magnitude 2Q and magnitude are located at.point (a,0,0) and (4a,0,0) .find the ratio of the flux of electric field due to these charges, through concentric spheres of radii 2a and 8a centred at origin .

Answer 1

Answer:

The ratio of the flux of electric field due to these charges is 2:1

Explanation:

Given that,

Radius of concentric spheres is

$r_{1}=2a$

$r_{2}=8a$

We draw the figure,

Using Gauss's law

Electric flux through small sphere of radius 2a

$\phi_{1}=\dfrac{2Q}{\epsilon_{0}}$ .....(I)

Electric flux through big sphere of radius 4a

$\phi_{1}=\dfrac{Q_{net}}{\epsilon_{0}}$

$\phi_{1}=\dfrac{2Q-Q}{\epsilon_{0}}$....(II)

Now, the ratio of the flux of electric field due to these charges

$\dfrac{\phi_{1}}{\phi_{2}}=\dfrac{2Q\times\epsilon_{0}}{Q\times\epsilon_{0}}$

$\dfrac{\phi_{1}}{\phi_{2}}=\dfrac{2}{1}$

Hence, The ratio of the flux of electric field due to these charges is 2:1