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An infinite number of charges having the quantum charge equal to q are placed along the x-axis at $x = 1, x = 2, x = 4$ and hence forth. Find the potential and electric field at the point x = 0, due to this set of charges

1 Answer

Finding potential
$V= \large\frac{1}{4 \pi \in_0} \frac{q}{x}$
Finding electric field
$E= \large\frac{1}{4 \pi \in_0} \frac{q}{x^2}$
$V= \large\frac{1}{4 \pi \in_0} \bigg[ \frac{q}{1} +\frac{q}{2} +\frac{q}{4} +.....$$ \infty \bigg]=\large\frac{2q}{4\pi \in_0}$
$E= \large\frac{1}{4 \pi \in_0} \bigg[ \large\frac{q}{1^2} +\frac{q}{2^2}+\frac{q}{4^2} +.....\bigg]$
$\quad= \large\frac{q}{4 \pi \in_0} \bigg[ 1+\large\frac{1}{4} +\frac{1}{16}+\frac{1}{64} +...... \bigg]$
$\quad= \large\frac{1}{4 \pi \in_0} \bigg[ \large\frac{4}{3} $$q\bigg]$
answered Jun 7, 2014 by meena.p