Gce Model Questions Vol1 2020 Physics Question 10

A point charge \(Q = 8.0\ \mu\text{C}\) is fixed at the origin of a coordinate system. A small isolated conducting sphere of radius \(a = 0.020\ \text{m}\) has its centre at the point \((0,0,0.050\ \text{m})\) on the positive \(z\)-axis. The sphere is initially uncharged and is allowed to reach electrostatic equilibrium. (a) Determine the magnitude of the total induced charge on the sphere (in microcoulombs, to one decimal place). (b) Find the magnitude of the electric field at point \(P\) located at \((0,0,0.10\ \text{m})\) on the same axis, expressed in scientific notation with two significant figures, and state its direction (towards or away from the origin). Use \(\varepsilon_0 = 8.85\times10^{-12}\ \text{F m}^{-1}\).