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Question:
If the repulsive force is moving the Charge away, and we apply some force and charge comes from A to B, if we're applying same amount of force that is equal to repulsive force then how can this charge move, same same force will not cancel out???
Answer:

Yes,it is correct that two forces of equal magnitude if applied on an object in opposite directions then,they cancel out effect of each other and as the result,the object remains at rest.

 But,if against the repulsive force(which moves the charge away) we applied some force to move this charge from a point A to B,then definitely the applied force is greater than that force.

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