# Coil Moving through a Magnetic Field

#### Lanc1988

1. The problem statement, all variables and given/known data

At t=0, a rectangular coil of resistance R = 2 ohms and dimensions w = 3 cm and L = 8 cm enters a region of constant magnetic field B = 1.6 T directed into the screen as shown. The length of the region containing the magnetic field is LB = 15 cm. The coil is observed to move at constant velocity v = 5 cm/s. What is the force required at time t = 0.8 sec to maintain this velocity?

F(0.8 sec) = ?? N

2. Relevant equations

3. The attempt at a solution

This problem has a walkthrough to help me solve it, however I have reached the end of the walkthrough and tried using the equation but it isn't working for me.

I find out the following in the walkthrough:

the change in flux (dF/dt) through the loop is 1.6*0.03*0.05

the current can be calculated using V=IR

and finally F = IwB

so for the answer I try: (.05/2)*.03*1.6 but it keeps saying that it is wrong.

#### Vuldoraq

Hi there,

Have you taken into account there are two parts of the wire perpendicular tot he B-field?

#### Lanc1988

As i go through the walkthrough it tells me that 2 of the wires cancel each other out and I am only left with needing to calculate the force on the wire of length w

#### Vuldoraq

My mistake, I didn't realise it only just entered the field. Try working this through algebraicaly first to obtain a final expresion for F, then put the numbers in. I think you should have a couple of squared quantities in there somewhere.

#### Lanc1988

but they tell me in the walkthrough that all of those equations are correct.. at the end im told that F = IwB and that I now have enough information to solve the equation for the final answer so I don't understand why it keeps telling me that my answer is wrong.

#### Vuldoraq

Yes, F=IwB. What does I=?

#### Vuldoraq

so for the answer I try: (.05/2)*.03*1.6 but it keeps saying that it is wrong.
According to this you have said that: current=velocity/resistance. This is not true in any circumstance.

#### Lanc1988

they told me to use the equation V=IR so the current should be equal to V/R.. how am i suppose to figure out what the current is then?

#### Vuldoraq

The flux through the coil that you calculated in your first post is equal to the emf generated in the coil by the motion through the b field.

The V in the expression of V=IR is always the voltage.

In this situation the only voltage contribution is from the emf generated in the wire, which you have already calculated.

#### Lanc1988

i see now.. when i saw V=IR without thinking about it i just put the v for the velocity.. it all makes sense now, thanks for your help.

#### Vuldoraq

Your welcome. Did it come out right in the end?

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