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PHYS1022 Electricity and Magnetism
Problem Sheet 1: tutorials
These problem sheets are designed to provide problems for you to discuss in tutorials
with your tutors. They should re-enforce the material we are studying in the lectures.
Problems for tutorials
1. Three equal positive point charges are situated at the corners of an equilateral triangle.
Sketch the electric field lines in the plane of the triangle.
2. Derive the formula s = ut + ½ at2 and explain its relevance to a charged particle in a
constant electric field. How would you proceed if the electric field were not constant?
3. The figure shows five pairs of plates: A, B and D are charged plastic plates and C is an
electrically neutral copper plate. The electrostatic forces between the pairs of plates are
shown for three pairs. For the remaining two pairs, do the plates repel or attract each
other? Explain your reasoning in each case, and draw the charges for the third pair.
4. The figure shows three electric field lines. What is
the direction of the electrostatic force on a positive test
charge placed at (a) point A and (b) point B?
At which point, A or B, will the acceleration of the test
charge be greater if the charge is released? Explain.
Solutions
1. The same number of field lines leave each charge; asymptotically it looks like a single
charge of 3q; a charge at the centre experiences no force.
2. For constant acceleration we may integrate
In a constant electric field a charge (of constant mass!) experiences a constant
acceleration (a = qE/m). If acceleration is not constant but depends on x then the first
integral is much harder!
3. A and B have opposite charge
A and D have the same charge
So B and D have opposite charge and attract.
Whatever Ds charge it will polarize the charge in the copper (eg a –ve charged D will
attract +ve charge to the near surface of C and send –ve charge to the far surface) and
they will attract.
4. The force is in the direction of the tangent to the field lines.
The strength of the force is proportional to the density of field lines.
(a) in positive x-direction
(b) positive x direction but negative y – along the field line
The acceleration is greatest at A where the lines are most dense.