- #1
GreatEscapist
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Homework Statement
Find an expression for the magnetic field inside a wire carrying a current density J = Cr2 where C is a constant to be determined in the problem. The total current in the wire is I and the radius of the wire is R. Your answer should be a function of r, R and I, but should not contain C.
Homework Equations
[itex]\oint\vec{B}*d\vec{s}[/itex]=[itex]\mu[/itex]0*Ithrough
J = dI/dA
I = dQ/dt
The Attempt at a Solution
I know that the first thing I need to do is solve for C in the J expression. I know that J = dI/dA. I want to integrate over the entire wire's radius, so I would want to integrate from 0 to R... the problem is I can't make my integral work. I tried Cr2 = ∫dI / dA, etc.
I actually think I can solve the rest of the problem myself, but I am stuck on the freaking calculus. Can someone help me set up this integral?