Question

Two point charges and are located apart in vacuum
(a) What is the electric field at the midpoint O of the line joining the two charges?
(b) If a negative test charge of magnitude is placed at this point, what is the force experienced by the test charge?

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Solution
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(a) The situation is represented in the given figure. O is the mid-point of line AB.

Distance between the two charges,

Net electric field at point

Electric field at point O caused by +3 C charge,

along OB

Where,

 Permittivity of free space

Magnitude of electric field at point O caused by - 3 C charge,

along OB

[As = , the value is multiplied with 2]

N/ C   along OB

Therefore, the electric field at mid-point O is  N/ C  along OB.


(b) A test charge of amount  is placed at mid-point O.

Force experienced by the test charge

The force is along line OA. This is because the negative test charge is repelled by the charge placed at point B but attracted towards point A.

Hence, the force experienced by the test charge is along OA.

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