Question

Two point charges $Q_1=8\times {10}^{-9}C$ and $Q_2=-6\times {10}^{-9}C$ are separated by $10$ cm in air. The intensity of electric field at the midpoint between the point charges is :

• A. $72\times {10}^{2}V/m$
• B. $5.04\times {10}^{4}V/m$
• C. $2.16\times {10}^{4}V/m$
• D. $2.44\times {10}^{4}V/m$

Answer 1

The correct option is B $5.04\times {10}^{4}V/m$

At midpoint $r=10/2=5$

We know electric field due to charge $Q_p=\frac{kQ}{r^2}$
Now E due to $Q_1=\frac{k{Q}_1}{r^2}=\frac{9\times {10}^9\times 8\times {10}^{-9}}{(5\times {10}^{-2}{)}^2}$
$=2\cdot 88\times {10}^4$
Now E due to $Q_2=\frac{k{Q}_2}{r^2}=\frac{9\times {10}^9\times (-6\times {10}^{-9})}{(-5\times {10}^{-2}{)}^2}$
$=-2\cdot 16\times {10}^4$
$\therefore totalE=(2\cdot 88+2\cdot 16)\times {10}^4$
$=5.04\times {10}^{4}V/m$