Question

An infinite number of charges each equal to q are placed along the $X-$ axis at $x=1,x=2,x=4,x=8$....... and so on. The potential and field respectively due to this set of charges at the origin is :

• A. $\frac{q}{3\pi {ϵ}_0}$ and $\frac{q}{2\pi {ϵ}_0}$
• B. $\frac{q}{2\pi {ϵ}_0}$and$\frac{q}{3\pi {ϵ}_0}$
• C. $\frac{q}{2\pi {ϵ}_0}$and$\frac{q}{4\pi {ϵ}_0}$
• D. $\frac{q}{4\pi {ϵ}_0}$and$\frac{q}{3\pi {ϵ}_0}$

Answer 1

Answer: (B)

Here, the required potential $V=\frac{1}{4\pi {ϵ}_0}[\frac{q}{1}+\frac{q}{2}+\frac{q}{4}+....]$

or $V=\frac{q}{4\pi {ϵ}_0}[1+\frac{1}{2}+\frac{1}{4}+....]$