(a)
The centres of two identical fixed conducting spheres each of charge +Q are separated by a distance D. C is the midpoint of the line joining the centres of the spheres.
(a.i)
Sketch, on the axes, how the electric potential V due to the two charges varies with the distance r from the centre of the left charge. No numbers are required. Your graph should extend from r=0 to r=D.
(a.ii)
Calculate the work done to bring a small charge q from infinity to point C.
Data given:
Q=2.0×10−3 C,
q=4.0×10−9 C
D=1.2 m
(b.i)
The magnitude of the net force on q is given by D332kQqx. Explain why the charge q will execute simple harmonic oscillations about C.
(b.ii)
The mass of the charge q is 0.025 kg.
Calculate the angular frequency of the oscillations using the data in (a)(ii) and the expression in (b)(i).
(c)
The charges Q are replaced by neutral masses M and the charge q by a neutral mass m. The mass m is displaced away from C by a small distance x and released. Discuss whether the motion of m will be the same as that of q.