Question

Two charges $5\mu C$ and $-20\mu C$ are placed $30cm$ apart. Find the strength of electric field at the midpoint between them.

• A. ${10}^{6}N{C}^{-1}$
• B. ${10}^{5}N{C}^{-1}$
• C. ${10}^{8}N{C}^{-1}$
• D. ${10}^{7}N{C}^{-1}$

Answer 1

The correct option is D ${10}^{7}N{C}^{-1}$

$x=\frac{r}{2}=15cm$

Field at P due to $Q_1$ is leftward being it a negative charge and the field due to $Q_2$ is also since it is a positive charge.

$E_1=\frac{Q_1}{4\pi {ϵ}_o{x}^2}+\frac{Q_2}{4\pi {ϵ}_o{x}^2}$

Since we have already decided the direction of field according to nature of charge , hence now we will only use magnitude of charge.

$E=\frac{1}{4\pi {ϵ}_o{x}^2}(Q_1+Q_2)$

$⟹E=\frac{9\times {10}^9}{(15\times {10}^{-2}{)}^2}(5+20)\times {10}^{-6}$

$⟹E={10}^{7}N{C}^{-1}$

Answer-(D)