Find the magnetic force on the square loop

AI Thread Summary
The discussion focuses on calculating the magnetic force on a square loop carrying a current when placed near a long wire. The relevant equations for magnetic force and magnetic field are provided, but initial attempts at solving the problem resulted in incorrect answers. Participants emphasize the need to calculate the magnetic field at each segment of the loop and to consider the forces acting on each side. It is noted that the forces on certain segments will cancel each other out due to symmetry. The conversation concludes with a participant expressing gratitude for assistance and a commitment to revisit the problem after further study.
Abs
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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.
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Abs said:
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 FPQ and FRS
 
Abs said:

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?
 
SammyS said:
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
 
Hesch said:
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
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)
 
Abs said:
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 FSP, and so on.
 
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Hesch said:
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.
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 ?
 
Abs said:
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 FRS and FPQ will be symmetrical and counter-acting. So forget them.
Abs said:
After I find all the Force(s) do I add them ?
Yes. Be careful with directions.
 
Hesch said:
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.
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
 
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