Question

Two charged particles A and B have charges $+10\mu C$ and $+40\mu C$ are held at a separation of $90cm$ from each other. At what distance from A, electric field intensity will be zero?

• A. $30m$
• B. $30mm$
• C. $30cm$
• D. $30km$

Answer 1

The correct option is C $30cm$

$E_A=\frac{k{q}_A}{x^2}$ rightward

And $E_B=\frac{k{q}_B}{(l-x{)}^2}$ leftward

Since, there is no field at P.

$E=E_A-E_B=0$

$⟹kq(\frac{q_A}{x^2}-\frac{q_B}{(l-x{)}^2})=0$

$⟹{\left(\frac{l-x}{x}\right)}^2=\frac{q_B}{q_A}$

$⟹\frac{l-x}{x}=\sqrt{\frac{40}{10}}=2$

$⟹l-x=2x$

$⟹x=\frac{l}{3}=\frac{90cm}{3}$

$⟹x=30cm$

Answer-(C)