Current induced in loop - treat like a solenoid?

[yeahhyeahyeah]

Homework Statement

A long straight wire lies below to a circuluar loop of wire. The straight wire is carrying a constant 10A current to the right. What is the magnitude and direction of the current in the circular loop, if its diameter is 1 m and its center is 0.75m away from the wire

Homework Equations

B = u i / 2pir

B = u i N for solenoid

The Attempt at a Solution

B = ui/2pir
since current in wire is traveling right and the loop is above the wire, the magnetic field on the loop is going to be coming out of the screen, I'm going to assume that the magnetic field is uniform, using the distance from the center as the radius, even though.. that is probably a bad assumption?

so the current will travel counterclockwise

can't figure out how to find the magnitude though! should i be treating it like a solenoid, and plug in the magnetic field to get a current?

 

[Nate810]

B = ui/2pir = (4pix10^-7)(10)/2pi(0.75)= 0.213 TB = uiN N = 4pix0.75/2pi = 0.47 turnsI = B/uN= (0.213 T)/(4pix10^-7 x 0.47 turns)= 2.71 A

 

[nlightner]

I would approach this problem by first considering the basic principles of electromagnetism. The magnetic field created by a long straight wire is given by the equation B = u i / 2pir, where u is the permeability of the medium (in this case, air), i is the current in the wire, and r is the distance from the wire.

In this case, we are interested in the magnetic field at the center of the circular loop, which is 0.75 m away from the wire. Plugging in the values, we get B = (4π x 10^-7 Tm/A) x 10 A / (2π x 0.75 m) = 5.33 x 10^-6 T.

Next, we can use the fact that the magnetic field at the center of a circular loop is given by B = u i N, where N is the number of turns in the loop. Since the current in the wire is creating a magnetic field of 5.33 x 10^-6 T at the center of the loop, we can set this equal to B = u i N and solve for N. We get N = B / (u i) = (5.33 x 10^-6 T) / (4π x 10^-7 Tm/A x 10 A) = 1.34 x 10^4 turns.

Therefore, the magnitude of the current induced in the circular loop is 1.34 x 10^4 A, and it will travel counterclockwise. This is significantly larger than the current in the straight wire, which makes sense since the circular loop has a larger area and therefore can generate a stronger magnetic field.

In conclusion, while we can use the equation for a solenoid to find the number of turns in the circular loop, we do not need to treat it as a solenoid in this case. Instead, we can use the basic principles of electromagnetism to solve the problem.