Question

A wire of linear charge density $\lambda$ passes through a cuboid of length $\ell$, breadth $b$ and height $h(\ell >b>h)$ in such a manner that flux through the cuboid is maximum. The position of the wire is now changed, so that the flux through the cuboid is minimum. The ratio of maximum flux to minimum flux will be :

• A. $\frac{\sqrt{l^2+b^2}}{h}$
• B. $\frac{\sqrt{l^2+b^2+h^2}}{h}$
• C. $\frac{h}{\sqrt{l^2+b^2}}$
• D. $\frac{l}{\sqrt{l^2+b^2+h^2}}$

Answer 1

The correct option is B $\frac{\sqrt{l^2+b^2+h^2}}{h}$

Formula,

$Q=\frac{q}{{ϵ}_0}$

maximum flux occurs diagonally,

$Q_{max}=\frac{\sqrt{L^2+B^2+H^2}}{{ϵ}_0}$

minimum flux occurs when height equals length,

$Q_{min}=\frac{H}{{ϵ}_0}$

the ratio of maximum by minimum flux is given by,

$\frac{Q_{max}}{Q_{min}}=\frac{\frac{\sqrt{L^2+B^2+H^2}}{{ϵ}_0}}{\frac{H}{{ϵ}_0}}$

$\therefore \frac{Q_{max}}{Q_{min}}=\frac{\sqrt{L^2+B^2+H^2}}{H}$