Inductive Heater Homework: Find Current & Rate of Energy

[Angie K.]

Homework Statement

A 34.6 -cm-diameter coil consists of 25 turns of circular copper wire 2.25 mm in diameter. A uniform magnetic field, perpendicular to the plane of the coil, changes at a rate of 3.55 × 10-3T/s. Determine

a. the current I in the loop,

b. and the rate dU/dt at which thermal energy is produced.

Homework Equations

magnetic flux = B*A cos Theta

I = magnetic flux / R

R = p (L/A) where p is the resistivity of copper

The Attempt at a Solution

Here is what I attempted:

First, I found the magnetic flux by using the formula: B*A cos Theta

multiplying the area by 25 because it's in a coil and using .173 meters for the radius of the coil

(3.55*10^-3)(25*.173) = 1.535375*10^-2

then to find I (current) :

I = magnetic flux / resistance

I calculated resistance by :

since it's a coil, I multiplied the L by 25 and the A by 25

R = p (L/A) = 1.68*10^-8 (25*pi*.173 / 25*pi*1.125*10^-2)^2 = 0.001148

plugging in that into the I equation, I = 1.535375e-2 / 0.001148 = 13.374 A

This isn't the right answer and I messed something up. I would appreciate if someone could help me with catching my mistake! I appreciate it!

Thanks in advance!

 

[AdityaDev]

again. why do you say that i=magnetic flux/R ?
$E=-d\phi/dt$.
so i is the change in magnetic flux per unit time/R.
what is the area of cross section of wire?

 

[Angie K.]

again. why do you say that i=magnetic flux/R ?
$E=-d\phi/dt$.
so i is the change in magnetic flux per unit time/R.
what is the area of cross section of wire?

I meant to say that i = emf/R

The area of the cross section is pi*r^2 which is pi(.00225)^2 where .00225 is the radius of the wire

= 1.590431e-5

Would I only multiply the circumference of the coil by 25?

 

[AdityaDev]

no. 2.25 is its diameter.

 

[Angie K.]

no. 2.25 is its diameter.

Oh that's right! My bad.

R = p (L/A) = 1.68*10^-8 (25*pi*.173 / pi*(0.00225/2)^2 = .11482

then I = Emf/R = B*Area of coil / R = 3.41194*10^-2 / .11482 = 0.297155 A

Still not getting it right. When calculating for the Emf, did I do that right? or is the fact that i's a changing magnetic field need some different calculation to get the Emf?

 

[AdityaDev]

what is the total length of wire? your value of L in R=p(LA) is wrong.