Find the magnetic force on the square loop

[Abs]

Homework Statement

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.

Homework Equations

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

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.

 

[Hesch]

I tried finding B [by (2) ]and putting it in the equation (1)

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

Hint: Consider the forces F_PQ and F_RS

 

[SammyS]

Homework Statement

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.

Homework Equations

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

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.View attachment 86512

Hello Abs. Welcome to PF !

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

 

[Abs]

Hello Abs. Welcome to PF !

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

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

 

[Abs]

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

Hint: Consider the forces F_PQ and F_RS

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)

 

[Hesch]

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

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 F_SP, and so on.

 

[Abs]

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 F_SP, and so on.

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 ?

 

[Hesch]

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

As for RS and PQ the B-field will not be homogeneous, but anyway the forces F_RS and F_PQ will be symmetrical and counter-acting. So forget them.

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

Yes. Be careful with directions.

 

[Abs]

As for RS and PQ the B-field will not be homogeneous, but anyway the forces F_RS and F_PQ will be symmetrical and counter-acting. So forget them.

Yes. Be careful with directions.

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