Magnetic Flux Through a Coil

[ttiger2k7]

Homework Statement

A long straight wire on the z-axis carries a current of 3.0 A in the positive direction. A circular loop in the xy-plane, of radius 10 cm, carries a 5.0-A current, as shown. Point P, at the center of the loop, is 25 cm from the z-axis.

A circular coil of four turns, 2 cm in diameter, is placed in the xy-plane with its center at P. The magnetic flux through the coil is closest to:

a)4.9 x 10-9 Wb
b)9.9 x 10-9 Wb
c)4.0 x 10-9 Wb
d)1.5 x 10-9 Wb
e)2.0 x 10-9 Wb

Homework Equations

$$B=\frac{\mu_{0}Ia^2}{2(x^2+a^2)^{3/2}}$$ (on the axis of a circular loop)$$B=\frac{\mu_{0}NI}{2a}$$ (at the center of N circular loops)$$\Phi=\int$$B*dA (magnetic flux)

The Attempt at a Solution

So I tried finding the magnetic flux of the loop first in the image given. First I needed the field of the loop:

Using the first formula, I used I = 5 A, x = .25 m, a = .01 m. My final answer resulted in : 2.01E-8 T

Then, I used the formula for magnetic flux, using 2.01E-8 T for B, and the area of this circle.

Area of circle: $$2\pi*r^2$$, where r will be .01
$$2\pi*.01^2$$ = 6.28E-4

so

$$\Phi$$ = 2.01E-8 * 6.28 E-4 = 1.26 E -11

***

I figure that somehow, I needed the magnetic flux of the loop to figure out what the flux of the coil would be. Am I even approaching this correctly?

 

[Shooting Star]

The Attempt at a Solution

So I tried finding the magnetic flux of the loop first in the image given. First I needed the field of the loop:

Using the first formula, I used I = 5 A, x = .25 m, a = .01 m. My final answer resulted in : 2.01E-8 T

You should put x=radius of the loop, a=0. Do you know what x and a represent? Consult your notes or book.

Where is the field due to the straight wire? You have to include that too.

After finding the total B at the centre, think about finding the flux.

 

[Moetasim]

Your approach is correct. To find the magnetic flux through the coil, you first need to find the magnetic field at the center of the coil, which you have done correctly. Then, you can use the formula for magnetic flux, \Phi = \int B*dA, to find the flux through the coil.

In this case, the coil is made up of four turns, so you will need to multiply the magnetic field at the center of the coil by 4 to account for the four turns. Then, you can use the area of the coil, which is \pi*r^2, where r is the radius of the coil (0.01 m). This will give you the total magnetic flux through the coil.

So, the correct answer would be 4 * (2.01E-8 T) * (pi * 0.01^2) = 2.01E-10 Wb, which is closest to option d) 1.5 x 10^-9 Wb.