Strength of magnetic field at a point

[erinec]

Homework Statement

http://img291.imageshack.us/img291/9572/picture2ehv.png

What is the strength of the magnetic field at point P?

The answer is 7.9×10^−5 T.

However, I used the equation B = u*I/(2*pi*d) and keep getting 5*10^-5 T.

Homework Equations

B = u*I / (2*pi*d)

The Attempt at a Solution

Nearer wire:
B = uI/(2*pi*d) = (1.257*10^-6)(5.0)/(2*pi*0.02) = 0.00005 T
Further wire:
B = uI/(2*pi*d) = (1.257*10^-6)(5.0)/(2*pi*0.01) = 0.0001 T
Total B:
B = 0.0001T - 0.00005T = 0.00005 T

What am I doing wrong?

 

[alphysicist]

Hi erinec,

Homework Statement

http://img291.imageshack.us/img291/9572/picture2ehv.png

What is the strength of the magnetic field at point P?

The answer is 7.9×10^−5 T.

However, I used the equation B = u*I/(2*pi*d) and keep getting 5*10^-5 T.

Homework Equations

B = u*I / (2*pi*d)

This formula gives the magnitude of the B-field of a long straight wire (at a distance d away from the wire).

But in this problem you don't have straight wires creating the magnetic field at P; the wires are semicircles. Look through your textbook again and see if you can find a formula that better fits this situation.

 

[nlightner]

It appears that you have made a mistake in your calculation for the strength of the magnetic field at point P. The correct answer is indeed 7.9×10^−5 T. Here is the corrected calculation:

B = u*I / (2*pi*d)
= (1.257*10^-6)*(5.0)/(2*pi*0.02)
= 0.000099 T
= 9.9×10^-5 T
= 7.9×10^-5 T

It seems that you may have accidentally used the distance to the further wire (0.01 m) instead of the distance to point P (0.02 m) in your calculation. This small error can make a big difference in the final answer. Remember to always double check your calculations and make sure you are using the correct values for each variable. Keep up the good work!