Question

Consider two solid spheres of radius R with uniformly distributed charge throughout their volumes. Point
P lies on the line connecting the centres of the spheres and is located at a distance of 0.5R from the centre
of sphere 1 as shown. If the net electric field at P is zero, what is the ratio Q2/Q1 of the total charge on each
sphere.

Answer 1

The ratio of the total charge on the charges, Q2/Q1 is; 9

Electric field and Total Charge

The electric field due to a charge is directly proportional to its magnitude and inversely proportional to the square of the distance to such point;

Since, E1 = E2, it follows that;

• Q1/(d1)² = Q2/(d2)²

Where, d1 = 0.5 and d2 = 1.5

• Q1/(0.5)² = Q2/(1.5)²

• Q1/0.25 = Q2/2.25

• Hence, Q2/Q1 = 2.25/0.25

Q2/Q1 = 9.

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