Homework Help: Magnetic Field in an Infinitely Long Copper Rod

Xnipes · Nov 26, 2011

1. The problem statement, all variables and given/known data

A long, solid, copper rod has a circular cross-section of diameter 10.0 cm. The rod has a current of 5.0 A, uniformly distributed across its cross-section. Calculate the magnetic field strength at:

a) the centre of the rod
b) 2.5 cm from the centre
c) 5.0 cm from the centre
d) 7.5 cm from the centre

2. Relevant equations

This is supposed to be done somehow using B = μ/2∏ * I/r

I don't have any calculus knowledge.

3. The attempt at a solution

I've tried many ways, but nothing has been consistent. I assume that I need to figure out the value of I at each different point of the copper rod, which I've tried doing through all this finicky work with area and all this stuff, but I truly don't understand what I'm doing.

danielakkerma · Nov 27, 2011

Hey,
You stated that,

I don't have any calculus knowledge.

.
That's going to be very problematic, and a damper on your solving equations here;
You'll have to consider http://en.wikipedia.org/wiki/Ampere%27s_Law#Integral_form.
Also, remember that you're told that the current is distributed evenly across the cross section, or surface area, in other words, I' = (I/A)*A'(r), where A' is the local area, or, to be precise,
(I/R^2)*r^2, r<=R, where r is the distance from the center, and R=D/2;
So you ought to get, B*2*Pi*r=mu_0*(I/R^2)*r^2.
Master calculus, it's imperative,
Good luck,
Daniel

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Homework Help: Magnetic Field in an Infinitely Long Copper Rod

Xnipes

danielakkerma