Question

A rectangular loop of wire with width w = 2.50 cm and height h 5.00 cm is placed as pictured here a distance a- 1.50 cm from a wire carrying a time-dependent current I- kt2 where k- 354 A/s2. What is the EMF in the wire at t = 3.00 s? @ 20.8 μν counter-clockwise @ 62.5 μν counter-clockwise 10.4 μν clockwise 62.5 μν clockwise 20.8 μν clockwise 10.4 μν counter-clockwise

Answer 1

Given

w -2,50cm0,025m

$I=kt^{2}$

The magnetic field produced by the infinite wire at r distance is given by

$B=\frac{\mu_{o}}{4\pi}\frac{I}{r}$

The flux through the rectangle is given

$\Phi=\int_{a}^{a+w} Bhdr=\int_{a}^{a+w}\frac{\mu_{o}}{4\pi}\frac{I}{r}h dr$

or,

or,

The EMF of the wire is given by

dt

or,

$\epsilon =-2\frac{\mu_{o}}{4\pi}kth\times ln\frac{a+w}{a}=-\frac{\mu_{o}}{2\pi}kth\times ln\frac{a+w}{a}$

The emf in the wire at t=3.00s is given by

$\epsilon =-\frac{4\pi \times 10^{-7}}{2\pi}\times 354\times 3\times 0.05\times ln\frac{0.015+0.025}{0.015}$

or,

or,

(Counter-clockwise)

The EMF is at t=3s is $10.4\mu V$ counter-clockwise.

Answer 2

i-kt tuo 27 at 27 20 . 8 メ人V j in anti-clockwise