First slide

Electric field

Question

Three charges, each of +4 $μC$ are placed at the corners B, C and D of a square ABCD of side 1 m. The electric field at the center O of the square is

Moderate

A

7.2 x 10⁴ N/C towards A
B

7.2 x 10⁴ N/C towards C
C

3.6 x 10⁴ N/C towards A
D

3.6 x10⁴ N/C towards C

Solution

Here we shall use a logical trick. If a charge of 4 $μ$ C had also been placed at A then
$\begin{aligned} {\vec{E}}_{A} + {\vec{E}}_{B} + {\vec{E}}_{C} + {\vec{E}}_{D} = \vec{0} \\ \Rightarrow {\vec{E}}_{B} + {\vec{E}}_{C} + {\vec{E}}_{D} = - {\vec{E}}_{A} \end{aligned}$
$\begin{array}{l} \Rightarrow |{\vec{E}}_{B} + {\vec{E}}_{C} + {\vec{E}}_{D}| = \frac{k (4 \times 10^{- 6})}{(1 / \sqrt{2})^{2}} \\ \Rightarrow |{\vec{E}}_{B} + {\vec{E}}_{C} + {\vec{E}}_{D}| = (9 \times 10^{9}) (4 \times 10^{- 6}) (2) \\ \Rightarrow |{\vec{E}}_{B} + {\vec{E}}_{C} + {\vec{E}}_{D}| = 7 .2 \times 10^{4} {NC}^{- 1} \end{array}$
towards A

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