Magnetic field at the center of a loop

[Nicki]

Homework Statement

A conductor consists of a circular loop of radius
R = 14.4 cm
and two long, straight sections as shown in the figure. The wire lies in the plane of the paper and carries a current
I = 1.60 A.
Find the magnetic field at the center of the loop.

Homework Equations

biot-savart law
?

The Attempt at a Solution

I know I need use biot-savart law to get the field created by the loop, which is giving me 8.77 uT. This is apparently within 10% of the correct answer.
Do i need to find the current from the straight part of the wire too (superposition)?

I'm just not sure how to do this / what equations to use to do this?

 

[gneill]

Homework Statement

View attachment 79319
A conductor consists of a circular loop of radius
R = 14.4 cm
and two long, straight sections as shown in the figure. The wire lies in the plane of the paper and carries a current
I = 1.60 A.
Find the magnetic field at the center of the loop.

Homework Equations

biot-savart law
?

The Attempt at a Solution

I know I need use biot-savart law to get the field created by the loop, which is giving me 8.77 uT. This is apparently within 10% of the correct answer.
Do i need to find the current from the straight part of the wire too (superposition)?

Yes. And superpostiion is an excellent idea.

I'm just not sure how to do this / what equations to use to do this?

You should have an expression for the magnetic field at a given distance from a current-carrying wire...

 

[Nicki]

thats where I'm confused.

shouldn't i use B = (uI)/(2 pi r) ?
4pi x 10^-7 x 1.6A / 2 pi x .144m ? this gives me 2.22 uT which when added to the 8.77 is out the the correct range

 

[gneill]

thats where I'm confused.

shouldn't i use B = (uI)/(2 pi r) ?
4pi x 10^-7 x 1.6A / 2 pi x .144m ? this gives me 2.22 uT which when added to the 8.77 is out the the correct range

2.22 μT looks right for the straight wire. But the loop contribution looks a bit high to me. Can you show the details of your work there?

i need to take this integral of this don't i?

No, the expression gives the field magnitude, not a differential element. The integration was already done in deriving the expression.

 

[Nicki]

Ahhhh thank you! my mistake was in the calculation for the loop! i left the 4pi in place when using u/4pi

hahaah that was dumb. but thank you, i got the right answer. it's 9.20 uT!

:)