A single loop of wire with a radius R = 0.235m and a resistance of 15.0 ohms is

Question

A single loop of wire with a radius R = 0.235m and a resistance of 15.0 ohms is placed in a uniform magnetic field which points into the page. The magnitude of the magnetic field is linearly increased from B = 0.00 t to B = 1.57 T in a timespan of t = 0.200 seconds. Please answer the following questions (a) What is the direction of the induced current in the loop, clockwise or counterclockwise? Choose one. (b) What is the magnitude of the induced current in this loop while the magnetic field is increased? (c) Given this current from part b, how many electrons pass by a point in the loop in a time span of 0.100 seconds? (d) If a single proton (m _p = 1.67 times 10^-27 kg, q_p= 1.60 times 10^-l9) were observed to travel in a circular orbit with the same radius and magnetic field, what would is velocity be?

Explanation / Answer

R = 0.35 m , r = 15 ohm , B1 =T, B2 = 1.57 T

t =0.2 s

(a) clockwise

(b) from faradays law induced voltage = -d(phi)/dt

V = A(B2-B1)/t

V = I*r

I*15 = 3.14*0.35^2*1.57/0.2

I = 0.2 A

(c) s = 0.1 s

I = q/t =ne/t

0.2 = n*1.6*10^-19/0.1

n =1.25*10^17 electrons

(d) magnetic force = centripetal force

qvB = mv^2/r

qB = mv/r

1.6*10^-19*1.57 = 1.67*10^-27*v/0.35

v = 5.26*10^7 m/s

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