Question

A conducting rod of mass M slides without friction to the right on conducting rails. The rails are distance d apart and are connected by resistor R. A uniform, constant magnetic field of magnitude B points into the page. The rod has an initial velocity v_0. (No external, mechanical force is applied to the rod.)

a) What is the induced emf as a function of instantaneous velocity v? (Give your answer in terms of v and the given quantities.)

b) Current flows in a loop through the resistor, the rod, and the connecting rails. What are the magnitude and direction of the induced current as a function of velocity v?

c) What is the force on the rod? Give magnitude and direction.

d) Show that the velocity as a function of time is v(t) = v_0e^(-at) where a = B^2d^2/(MR)

e) What is the total energy dissipated in the resistor over all time?

Answer 1

Answer:

(a)  Induced emf (e) = Bvd

(b) Current = emf/R  Clockwise direction

(c) F = B²d²v/R

(d) Power (P) = B²d²v²/R

(e) Energy = B²d²v² t/R

Explanation:

Find attached of the calculation

(e) Total energy is calculated using the formula;

Energy = power *time

where power =  B²d²v²/R

Therefore,

Energy =  B²d²v²/R * t

            =  B²d²v² t/R