Question

(a) Write down the equations that relate: (i) The ?− component of the electric field at a point specified by position vector ? to the to the electric potential ?(?) at that point. (ii) The ?− component of the electrostatic force acting on a particle of charge ? to the ?− component of the electric field at the position of the particle. And hence deduce an expression for: (iii) The ?− component of the electrostatic force acting on a particle of charge ? in terms of the electrostatic potential energy ?el.

(b) Suppose that a proton of charge ?p is confined to the ?− axis in a region where the electric potential takes the form: ?(?)=?0 ?2 where ?0=2.5 V m−2 (i) Derive an expression (in terms of ?0, ? and ?p) for the electrostatic force experienced by the proton at a position ?. (ii) Explain carefully why your answer to (b) (i) implies that the proton undergoes simple harmonic motion. (iii) Calculate the period of the oscillation. ( 6 marks )

(c) Sketch an arrangement of two fixed charges that would give rise to oscillatory motion about the origin, for a small positive charge confined to the ?− axis. Sketch the field lines in the ??−plane resulting from this arrangement of fixed charges. You should indicate the sign of the charges but you do not need to give any magnitudes. ( 4 marks )

(d) Is the motion from the arrangement of charges in part (c) simple harmonic ? Explain your answer. ( 4 marks )

Answer 1