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Question

Four charges are arranged at the corners of a square as shown in the figure. The direction of electric field at the centre of the square is along :
468016_8fef4e90592f4096a713f296d2124d5e.png


A
DC
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B
BC
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C
AB
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D
AD
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Solution

The correct option is A DC
We can put an imaginary charge $$Q$$ at the center of the square and look at the forces acting on it due to the four charges.
Let the distance of each charge from the central charge is same.
Thus the magnitude of the force is proportional to the charge.
Force due to charge $$+q$$ is $$a \hat{i}-a\hat{j}$$
Force due to charge $$+2q$$ is $$-2a\hat{i}-2a\hat{j}$$
Force due to charge $$+3q$$ is $$-3a\hat{i}+3a\hat{j}$$
Force due to charge $$+4q$$ is $$4a\hat{i}+4a\hat{j}$$
Thus net force on the charge=$$4a\hat{j}$$
Thus the net direction of electric field at center is along DC.

Physics
NCERT
Standard XII

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