A loop of wire in the shape of a rectangle of width w and length l, and a long s

Question

A loop of wire in the shape of a rectangle of width w and length l, and a long straight wire carrying a current I are in a plane as shown. [Note: express all of your final answers in terms of l, w, r (defined in the figure), I_2 (defined below), numerical constants (such as pi), and constants that appear in Maxwell's equations.]

1. What is the magnitude and direction of the magnetic field at the exact center of the loop?

2. What is the magnetic flux through the loop due to current I? [Hint: You can't just multiply by an area; do an integral.]

3. If a current I_2 runs clockwise around the loop, what is the net force acting on the loop?

Answers:

1. (mu_0*I)/(2pi(r+w/2)), into the page

2. ((mu_0*I*l)/(2pi))*ln(1+w/r)

3. ((mu_0*I*I_2*l)/(2pi))(1/r-1/(r+w)), to the left

Really need help on this!! Explanation and formulas would be awesome! Thanks!

Explanation / Answer

FOLLOW THIS SOLVED EXAMPLE

Since the figure is both a straight wire as well as a loop, you would use the equations:


Bwire= (1e-7)* [(2I)/(r)]
Bloop= (1e-7)* [(2pi*R^2*I)/((z^2+R^2)^(3/2))], where z=0 in this case


You add these two equations together to get the correct answer:


Bloop + Bwire = approximate magnitude of the magnetic field


(1e-7)* [(2pi*R^2*I)/((R^2)^(3/2))] + (1e-7)* [(2I)/(r)] =


(1e-7)* [(2pi*.064^2*4.1)/((.064^2)^(3/2))] + (1e-7)* [(2*4.1)/(.064)] =



|B| = 4.0251e-5 + 1.2812e-5
|B| = 5.30641e-5


Direction is out of the page

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