Please answer BOTH questions as soon as possible. Thanks! 1)A single piece of wi

Question

Please answer BOTH questions as soon as possible. Thanks!

1)A single piece of wire is bent into the shape of Texas, with a total area of 3.41 cm2 . This Texas shaped loop is perpendicular to a magnetic field which increases uniformly in magnitude from 0.415 T to 2.19 T in a time of 2 s. The wire has a total resistance of 4 . What is the current? Answer in units of mA.

2)A 0.5465 mH inductor has a length that is four times its diameter. If it is wound with 23.6 cm1 turns per centimeter, what is its length? Answer in units of m.

Explanation / Answer

1)
The magnitude of the induced emf, e = A*B/t
We know,
I = v/R
I = (A*B/t)/R
I = (3.41*10^-4 *(2.19 - 0.415)/2.0)/4
I = 0.0757 mA

2)
L = 0.5465 * 10^-3 H
l = 4*d
Where d is the diameter.

N = 23.6 cm^-1
N = 23.6 * 100 Turns/m
N = 2360 Turns/m

Total No of Turns/meter, = 2360
Total No of Turns in Coil = 2360*l

L = (uo*N^2*A)/l
L = (uo*N^2*A*l)
0.5465 * 10^-3 = 4**10^-7 * 2360^2 * (1/4**d^2) * (4*d)
d = 0.0292 m
Length of the inductor, l = 4*0.0292 m
l = 0.1168 m

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