A square loop of side s is in a uniform magnetic field of strength B directed in

Question

A square loop of side s is in a uniform magnetic field of strength B directed into the paper. The shape of the loop is changed to a circle with the same perimeter in a time Delta t. Let s = 0.450 m, B = 2.50 T and Delta t = 0.0035 s. Find the magnetic of the average EMF around the loop (in V) while the change is taking place. a) 45.5 b) 62.0 c) 34.0 d) 39.5 If the resistance per unit length of the wire is 350 Ohm/m find the magnitude of the current I (in A) in the loop (in V) while the change is taking place. a) 0.0569 b) 0.0867 c) 0.0708 d) 0.0627 A cylinder of length s and diameter d is made of a material with resistivity rho. One end is connected to a conductor with potential V and the other end to a conductor at ground potential (0). Current is allowed to flow through the cylinder for a time t. let V = 10.0 V, s = 0.150 m, d = 0.0025 m. rho = 2800 Ohm middot m and t = 7.00 s. Find the resistance R (in Ohm) of the cylinder. a) 8.56 times 10^7 b) 7.36 times 10^7 c) 9.55 times l0^7 d) 6.24 times 10^7 For the cylinder in problem 9 find the current per unit area J (in A/m^2) through the cylinder, a) 1.13E + 06 b) 2.04E + 06 c) 6.24E + 05 d) 3.82E + 06 For the cylinder in problem 9 find the power dissipated in the cylinder (in W). a) 8.70 times 10^-7 b) 1.17 times 10^-4 c) 1.51 Times 10^-6 d) 5.77 times 10^-7 For the cylinder in problem 9, how many electrons pass through it in time t? a) 3.93 times 10^12 b) 5.11 times 10^12 c)6.12 times 10^12 d)6.61 times 10^12

Explanation / Answer

we know that the emf induced is given by

e = -d(phi)/dt = - d(BA)/dt = = B dA/st

e = B (A2 - A1)/t

A1 = s^2 = 0.450^2 = 0.2025 m^2

when a circle is formed,

2 pi r = 4s

r = 4s/2 pi = 4 x 0.45/2 x 3.14 = 0.287

A2 = pi r^2 = 3.14 x 0.287^2 = 0.2586 m^2

e = 2.5 (0.2586 - 0.2025)/0.0035 = 40 V (nearly equal to 39.5)

total length of wire = 4 s = 4 x 0.45 = 1.8 m

So total resistance, R = 1.8 x 350 = 630 Ohm

V = IR => I = V/R = e/R

I = 39.5/630 = 0.0627 A

Hence, (d) I = 0.0627 A is the most accurate answer.

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