Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: THEend8_
PHYS5140
Homework 7
Due: 9/12/2023 Sat (before 11:59 pm)
Submit your answers via Blackboard
Total marks= 110 (5 problems)
1. (10 marks) Consider a point charge q moving at a constant velocity v along the x-axis to
the positive x direction. At t=0, it is at (0,0,0). find the electric field at (x,0,0) and (-x,0,0) due
to the point charge.
Note: you may use the formula for electric field of a moving point charge without derivation.
2. Consider a rotating electric dipole composed of two equal but opposite point charges
moving along a circular path of radius b in the x-y plane at a fixed angular speed ω. (see p. 13
of Ch. 9 Lecture note (Part II)).
(a) (18 marks) Find the radiation fields (both electric and magnetic fields)
(b) (12 marks) Find the Poynting Vector and the total power radiated.
(c) (6 marks) Find the positions at which the radiation is circular polarized.
3. (14 marks) An electron is released from rest and falls under gravity. In the first centimetre,
what fraction of the gravitational potential energy is converted to radiation? (Neglect
radiation reaction force)
4. (20 marks) A particle of positive charge q moves with an initial velocity 0(≪ ) towards
another fixed positive charge Q. Initially, they are infinitely far away from each other. Due to
the repulsive force, the charge q decelerates as it approaches Q, and eventually returns out to
infinity. Find the energy radiated throughout the entire process. (Neglect radiation reaction
force).
Useful formula:
5. A particle of charge q moves along a circular path of radius R at a fixed angular speed ω
(ωR≪ ).
(a) (4 marks) Use Larmor’s formula to calculate the radiated power P.
(b) (12 marks) Find the radiation reaction force. Hence, find the work done by per unit time
due to that force.
(c) (14 marks) Repeat (a) and (b) for a particle performing simple harmonic motion () =
cosωt.