An elastic conducting material is stretched into a circular loop of radius r_o =

Question

An elastic conducting material is stretched into a circular loop of radius r_o = 10 cm. It is placed with its plane perpendicular to a uniform magnetic field of B = 0.90 T that acts into the page. When released, the radius of the loop starts to shrink at a constant rate of 2 mm/s. a.Write an expression for the radius, r, as a function of time, t. b.Write an expression for the magnetic flux,_B, as a function of time, t. c.Write an expression for the induced emf, epsilon, in the loop as a function of t. Determine epsilon at t = 10 s. d.If the resistance per unit length of the loop is 5 Ohm/m, what is value of the induced current in the loop at t = 10 s? In what direction (clockwise or counterclockwise) does the current flow?

Explanation / Answer

r0 = 0.1 m

a)

r = ro - 0.002t

b)

magnetic flux phi = B*A*coswt = B*pi*r^2*cos0

magnetic flux = B*pi*(r0-0.002t)^2

c)

induced emf = -rate of change in flux

E = dphi/dt

E = B*pi*(r0-0.002t)*2

at t = 10s

E = 0.9*pi*(0.1-(0.002*10))*2 = 0.4523 V

(d)

Resistacne R = 5*2*pi*r

at t = 10 s

R = 5*2*pi*(0.1-(0.002*10))

R = 2.513 ohms

current I = E/R = 0.4523/2.513 = 0.18 A

current direction is clockwise

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