In the above electricity question, we introduced the electrical potential on the positive
x-axis for a set of fixed charges, q1 and q2, as
(d) Using and extending this expression for V, calculate expressions for the electric
field along the (positive and negative) x-axis.
(e) Assuming that q1 = q2, make a rough plot of the electric field that you find as a
function of x. Justify your reasoning in creating your plot.
These questions follow on from Electromagnetism – Question 2. Initially Bart and Lisa are at rest
with respect to each other. However, after Lisa sends and Bart receives a 10 s long signal, they
ealise they are moving away from each other. The electromagnetic wave used to send the signal
has an intensity of 0.10 W/m2 and a frequency of 150 kHz.
(e) Explain carefully, with the aid of a diagram, what has caused this relative motion to occur.
(f) Calculate Bart’s final speed (relative to the frame in which he was initially at rest). Take the
diameter of the rod to be 1.0 cm and the combined mass of the rod, Bart and his space suit to
be 100 kg. State any other assumptions you need to make.
(g) Meanwhile Lisa, who together with her space suit also has a mass of 100 kg, finds that her
final speed, as measured in the frame in which she was initially at rest, is greater than that of
Bart’s. Explain how this could be so.
(e) For the time that the Hypatia is cruising at constant speed towards Luyten’s Star (i.e. the time
in between the acceleration and deceleration), how much time would have elapsed for NASA
on Earth according to the crew? Explain how your answer is consistent with the time that
NASA themselves would experience.
(f) The mass of the Hypatia is 120, 000 kg, and it has engines that run on matter-antimatter
annihilation. If the engines are 40% efficient, make a simple estimate of the mass of fuel that
would be required to be burnt to accelerate the Hypatia to its cruising speed. Neglect the mass
of the fuel in your calculation. Comment on your result.