Magnetic Induction and Magnetic Field

[roam]

Homework Statement

I would appreciate some help with the following problem:

http://img407.imageshack.us/img407/7647/questionb.jpg

Homework Equations

This is an equation derived from Biot-Savart law:

$B= \frac{\mu_0 I}{4 \pi s} \int^{\theta_2}_{\theta_1} cos \theta d \theta = \frac{\mu_0 I}{4 \pi s} (sin \ \theta_2 - sin \ \theta_1)$

Magnetic field of a solenoid: $B= \mu_0 \frac{N}{l} I$

N is the number of turns.

Magnetic field of a solenoid

The Attempt at a Solution

(a) Using the above equation above with R=L/2, θ₂=-θ₁=45°, and remembering that there are 4 sides, we find the magnetic field to be

$B=\frac{\sqrt{2} \mu_0 I}{\pi R}$

However this gives the "magnetic field" at the center of the loop, not the "magnetic induction". So, what exactly is the difference between magnetic induction and field? And what equation do I have to use in order to find the magnetic induction?

(b) Since the system forms a kind of solenoid I use the equation for the magnetic field of solenoid:

The total length og the wire is 20cmx4=80cm, 100x80=80000cm. So

(4∏x10^-7) (1/8) I = 50x10^-6

Solving for current yields I= 318.6 A. This value seems too large to be realistic. And the question again asks for magnetic induction, not the field. What equation do I have to use here?

 

[Simon Bridge]

Magnetic Field is sometimes called "Magnetic induction" - particularly in older textbooks.

(a) I'm puzzled that you used the polar form for the integral, since your problem has rectangular symmetry.

(b) You could also use the result from part (a) to help you.