Question

There are three concentric thin spheres of radius $a, b, c$ $( a > b > c )$. The total surface charge densities on their surfaces are $\sigma,-\sigma, \sigma$, respectively. The magnitude of electric field at $r$ (distance from centre) such that $ a > r > b $ is

• A. 0
• B. $\frac{\sigma}{\varepsilon_{0} r^{2}}\left(b^{2}-c^{2}\right)$.
• C. $\frac{\sigma}{\varepsilon_{0} r^{2}}\left(a^{2}+b^{2}\right)$
• D. none of these

Answer 1

Answer: (B)

Electric field at a distance $r( a > r > b)$ will be due to charges enclosed in $r$ only, and since a sphere acts as a point charge for points outside its surface,
$ \therefore E =\frac{k Q_{c}}{r^{2}}+\frac{k Q_{b}}{r^{2}}=\frac{k}{r^{2}}\left(\sigma \times 4 \pi c^{2}+(-\sigma) 4 \pi b^{2}\right)$|
$=\frac{\sigma}{\varepsilon_{0} r^{2}}\left(c^{2}-b^{2}\right) $