# Conducting rod creates a complete circuit

## Homework Statement

A conducting rod makes contact with rails to complete a circuit. If the rails are 50 cm apart ina uniform magnetic field B = 0.38 [T] directed out of the paper. The total resistance of the circuit is R = 9 [ohms] and is constant.
1) what is the magnitude and direction of EMF induced in the rod when it is moved to the left with a speed of 5 m/s
2) what force is required to keep the rod in motion (without acceleration)
3) how long would it take the rail to come to a stop?
4) what distance would it travel in that time?

e = Blv
I = e/R
F = ILB

## The Attempt at a Solution

1) e = Blv = 0.38 * 0.5 * 5 = .95 V
2) I = e/R = 0.95 / 9 = 0.106
F = 0.106 * .5 * .38 = 0.2N

I need help on number 3 and 4

Mark44
Mentor
Thread moved from Calculus section. This problem is more of a physics problem than a mathematics problem.

The description of the problem isn't clear to me. Is there a drawing that goes with this?

In the future, please post one or at most two problems per thread, not four or five as you have done in this and another thread you started.

Since you already calculated the force as a function of the rod's velocity in part (2), you can just apply Newton's second law in the form ##m\dot{v} = F##. This gives a simple differential equation for ##v(t)##. Once you have the solution, find ##T## such that ##v(T) = 0##--that's your answer to (3). (Hint: the answer may be a bit surprising.) To solve (4), just compute the integral ##\int_0^T v(t) dt##.

haruspex