PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A pair of low-resistance, frictionless conducting rails are separated by 0.40 m and connected to a small resistor of value 0.60 Ω. The arrangement lies horizontally in a region containing a uniform magnetic field of magnitude 0.25 T directed into the page.
At time t = 0, a conducting rod of negligible resistance is at rest at the left end of the rails. Beginning at that instant, an external mechanism causes the rod to move to the right so that its speed varies with time according to v(t) = (0.80 m s⁻²) t, where t is measured in seconds.
(1) Write an expression for the induced emf as a function of time for the interval 0 ≤ t ≤ 3.0 s.
(2) Calculate the magnitude of the emf at t = 3.0 s.
(3) Determine the total electric charge that passes through the resistor during the time interval 0 ≤ t ≤ 3.0 s.