Question

Two spheres of radii 30 cm and 40 cm contain
charges of 30 uC and 40 uC respectively. They
are seperated by a distance of 100 cm. Where
will be the field E be zero?
​

Answer 1

Two spheres of radii 30 cm and 40 cm contain charges of 30 uC and 40 uC respectively. They are seperated by a distance of 100 cm.

Let at a distance of r from first sphere, electric field intensity becomes zero.

where r in such a way that r > 40cm >30cm and also (100 - r) > 40cm > 30cm

so from Gauss law,

electric field due to first sphere, E1 = Kq1/r²

= k(30uC)/r²

electric field due to 2nd sphere , E2 = kq2/(100 - r)²

= k(40uC)/(100 - r)²

since, E1 and E2 are in opposite directions.

so, net electric field = E1 - E2 = 0

or, E1 = E2

or, K(30uC)/r² = K(40uC)/(100 - r)²

or, 3/r² = 4/(100 - r)²

or, √3/r = 2/(100 - r)

or, 100√3 - √3r = 2r

or, r = 100√3/(2 + √3) = 100√3(2 - √3)

or, r = 100(2√3 - 3) cm ≈ 46.41cm

hence, electric field intensity becomes zero at a distance of 46.41 from first sphere.