Electric field question: The answer is +4Q. Can you explain why? Thank you :) An

Question

Electric field question:

The answer is +4Q. Can you explain why? Thank you :)

An equilateral triangle has three vertices A, B, C which are equidistant from the centre O, as shown in the diagram. Positive charges of magnitude Q are placed at each of the vertices, creating an initial electric field at point O. Now a fourth charge of -Q is placed at point D, exactly midway between A and O. What value of charge must be added to the original charge at A, in order to return the electric field at O to the initial value E_i?

Explanation / Answer

Since the setup was symmetrical before charge at D was put, the electric field Ei was zero. so for all calculations the charges at A B and C can be ignored.

But now there is a charge at D.

The field due to A at O would be one fourth due to same charge at D because the distance is double.

So to compensate that we need four times the charge at A.

So the charge at A should be 4Q. the sign is positive because it needs to cancel the field at O by D.

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