Three charges each q are kept at 3 corners of a square as shown in fig and q /2 is at one corner . Electric field at the centre is

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Solution

Step 1: Given
Three charges of charge $q$ each.
Fourth charge $\frac{q}{2}$

Step 2: Calculation of electric field at centre

We know that electric field is given by
$∣ ∣ \to E ∣ ∣ = \frac{K q}{r^{2}}$

Electric field at centre O due to charges is
$E_{n e t} = E_{A} + E_{B} + E_{C} + E_{D}$
Now,
$∣ ∣ {\to E}_{A} ∣ ∣ = ∣ ∣ {\to E}_{B} ∣ ∣ = ∣ ∣ {\to E}_{C} ∣ ∣ = \frac{K q}{l^{2}}$ (since chage on corners A, B and are equal)
$∣ ∣_{D} ∣ ∣ = \frac{k q}{2 l}$
Since, the directions of the electric field $_{A} a n d_{C}$ are opposite, therefore,
$_{A} +_{C} = 0$
$∣ ∣ {\to E}_{n e t} ∣ ∣ = ∣ ∣ {\to E}_{B} ∣ ∣ - ∣ ∣ {\to E}_{D} ∣ ∣$
$∣ ∣ {\to E}_{n e t} ∣ ∣ = \frac{k q}{l^{2}} - \frac{k q}{2 l^{2}}$
$∣ ∣ {\to E}_{n e t} ∣ ∣ = \frac{k q}{2 l^{2}}$

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