First slide

Electric field

Question

Two charges $+ 5 μC$ and $+ 10 μC$ are placed 20 cm apart. The net electric field at the mid-Point between the two charges is

Moderate

A

$4 .5 \times 10^{6} N / C directed towards + 5 μC$
B

$4 .5 \times 10^{6} N / C directed towards + 10 μC$
C

$13 .5 \times 10^{6} N / C directed towards + 5 μC$
D

$13 .5 \times 10^{6} N / C directed towards + 10 μC$

Solution

From following figure,
$E_{A} = Electric field at mid point M due to + 5 μC charge$
$= 9 \times 10^{9} \times \frac{5 \times 10^{- 6}}{(0 .1)^{2}} = 45 \times 10^{5} N / C$
$E_{B} = Electric field at M due to + 10 μC charge$
$= 9 \times 10^{9} \times \frac{10 \times 10^{- 6}}{(0 .1)^{2}} = 90 \times 10^{5} N / C$
Net electric field at
$M = |{\vec{E}}_{B}| - |{\vec{E}}_{A}| = 45 \times 10^{5} N / C = 4 .5 \times 10^{6} N / C,$
in the direction of $E_{B} i . e . towards + 5 μC charge$

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