# Find the magnetic force on the square loop

1. Jul 28, 2015

### Abs

1. The problem statement, all variables and given/known data
A square loop PQRS carrying a current of 6A is placed near a long wire carrying 10A as shown in the figure. Find the magnetic force on the square loop.

2. Relevant equations
F = B * i * l ....................... (1)
B = (µ0 * i)/2 π r

3. The attempt at a solution
I tried finding out the answer by applying the formulas given above, I tried finding B [by (2) ]and putting it in the equation (1) but I did not get the correct answer.
BTW the answer is
1.6 x 10^-5 towards right.

2. Jul 28, 2015

### Hesch

You must find the B-field at the wires PQ, QR, RS and SP. Then find and add the forces.

Hint: Consider the forces FPQ and FRS

3. Jul 28, 2015

### SammyS

Staff Emeritus
Hello Abs. Welcome to PF !

What did you get for the answer, and what are the details of how you got it?

4. Jul 28, 2015

### Abs

I got 1.22 x 10^4

I first found out the magnetic force on P then S then Q and then R and took a mid point in the center of the square and I got four values and I found their arithematic mean and I got 1.22 x 10^4

5. Jul 28, 2015

### Abs

But we are supposed to find the force, then what good would it be to find force excewpt that it can be put in eqn (1)

6. Jul 28, 2015

### Hesch

Using F = B*I*L will not give any force at a mid point, which has a length = 0.
Force = B-field * current * Length of wire.

So find the B-field along the length SP, and find by use of (1) the force FSP, and so on.

7. Jul 28, 2015

### Abs

Wow, I made a big blunder there is nothing in the middle to be magnetized damn that was stupid of me.
Thanks Hesch
Just one more question,

When I find B by B = (µ0 * i)/2 π r

Do I have to find it for SR and PQ ? If yes then how do you find it in a horizontal wire ? I know how to find it in a vertical wire

AND

After I find all the Force(s) do I add them ?

8. Jul 28, 2015

### Hesch

As for RS and PQ the B-field will not be homogeneous, but anyway the forces FRS and FPQ will be symmetrical and counter-acting. So forget them.
Yes. Be careful with directions.

9. Jul 28, 2015

### Abs

Biiiiiiig thanks Hesch I don't get it why are you so smart man I am jealous. Thanks.
I will tell you positively by tomorow if I get the answer(it is my time to sleep now then school tutions ..... etc)
Bye