Answer to Question #211970 in Electricity and Magnetism for Anita

Question

The electric flux density on a spherical surface r 5 b is the same for a point charge Q located at the origin and for charge Q uniformly distributed on surface r 5 a1a , b2. (a) Yes (c) Not necessarily (b) No

Answer 1

Electric flux density=$\smallint E.da=\smallint E.dacos\theta$

$\phi=\smallint E.dAcos\theta$

$\phi=E.A$

$\theta=0°$

r=b

Q charge distribution at sphere radius r=b

$\phi=\frac{kQ}{b^2}\times4\pi b^2$

$\phi=\frac{Q}{\epsilon_0}\rightarrow(1)$

r=a

Q charge distribution at sphere radius r=a

$\phi=\frac{kQ}{a^2}\times4\pi a^2$

$\phi=\frac{kQ}{a^2}\times4\pi a^2=\frac{Q}{\epsilon_0}\rightarrow(2)$

equation (1) and (2) are equal

Then electric flux density does not depend on size shape of sphere

Option (b) is correct option