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  4. Four charges are rigidly fixed along the Y-axis as shown. A positive charge approaches the system along the X-axis with initial speed just enough to cross the origin. Then its total energy at the origin is

Q. Four charges are rigidly fixed along the Y-axis as shown. A positive charge approaches the system along the X-axis with initial speed just enough to cross the origin. Then its total energy at the origin isPhysics Question Image

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Solution:

There exists a point P on the x-axis (other than the origin), where net electric field is zero. Once the charge Q reaches point P, attractive forces of the two -ve charge will dominate and automatically cause the charge Q to cross the origin. Now if Q is projected with just enough velocity to reach P, its K.E. at P is zero, but while being attracted towards origin it acquires K.E. and hence its net energy at the origin is positive. (P.E. at origin = zero)