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  4. Consider two spheres of the same radius R having uniformly distributed volume charge density of same magnitude but opposite sign (.+ρ and -ρ .. The spheres overlap such that the vector joining the centres of the negative sphere to that of the positive sphere is overset arrow d(d ll R). The magnitude of the electric field at a point outside the spheres at a distance r in a direction making an angle θ with overset arrow d is found to be (ρ /a ((ϵ )0))((R3 d/r3))√b (cos)2 θ + 1. The value of (.a+b.) is (Distance r is measured with respect to the mid point of the line joining the centers of the two spheres.)

Q. Consider two spheres of the same radius having uniformly distributed volume charge density of same magnitude but opposite sign and The spheres overlap such that the vector joining the centres of the negative sphere to that of the positive sphere is The magnitude of the electric field at a point outside the spheres at a distance in a direction making an angle with is found to be The value of is (Distance is measured with respect to the mid point of the line joining the centers of the two spheres.)

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Solution:

For writing field at an outside point, we can consider the charge on each sphere to be located at respective centre. Thus we have a dipole of dipole moment

Where
Field at


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