# Current Carry Wire With A Loop

Charanjit
1. Homework Statement :
A. Determine the magnetic flux through a square loop of side a (see the figure) if one side is parallel to, and a distance b from, a straight wire that carries a current I.

Express your answer in terms of the variables I, a, b, and appropriate constants.

B. If the loop is pulled away from the wire at speed v, what emf is induced in it?
Express your answer in terms of the variables I, a, b, v, and appropriate constants.

2. Homework Equations :
Flux=integral(B*da)
E=BLv

I think those are the two equations we need, but not 100% sure.

3. The Attempt at a Solution :
I have already figured out part A, and the solution is posted above, just having issue with part B.

So all I did was replaced L=length with "a", one side of the area. I am totally lost here. So please help me.

## Answers and Replies

Homework Helper
Gold Member
Have you tried using Faraday's law?

Charanjit
Well yes, but how to relate velocity?

Homework Helper
Gold Member
Well yes, but how to relate velocity?

The rate of change per unit time of $$\Phi_B$$ is a function of the loop's velocity.

Hint: Distance = Velocity times Time. Distance here, as your problem describes it, is your variable 'b'. Next find the negative of the time derivative of $$\Phi_B$$.

Charanjit
Which b are you talking about? The equation E=BLv? That "B" is the magnetic field.

Homework Helper
Gold Member
Which b are you talking about? The equation E=BLv? That "B" is the magnetic field.

In the problem statement, "...and a distance b from ..."

Charanjit
Ok... so how do I import that into the equation? We don't have the "time" variable.

Homework Helper
Gold Member
Ok... so how do I import that into the equation? We don't have the "time" variable.

Distance is equal to Time times Velocity, or b = vt.

Make the substitution as an interim step. You can always make the reverse substitution (t = b/v) later to get rid of the 't' variable if you need to, once you have your final answer.

Charanjit
Ok, but in which equation? E=BLv?

Homework Helper
Gold Member
Ok, but in which equation? E=BLv?

try the answer to the first part: