Fabio Phys 208 H (8%) Problem 6: A rod AB with length L 0.16 m is lying on a rec

Question

Fabio Phys 208 H (8%) Problem 6: A rod AB with length L 0.16 m is lying on a rectangular conducting loop of zero resistance in a magnetic field as shown in the figure. The x x x x x x magnetic field has a constant magnitude Bi 0.75 T. The rod is moving to the right with speed v 0.69 m/s. The resistance on AB is R 140 2 X X X X X X Randomized Variables X X X X X X La 0.16 m x x 1 x x x 2 B 0.75 T v 0.69 m/s 140 Otheexpertta.com 10% Part (a) Express the change of the magnetic flux going through the loop 1,4p1.in terms of B, v, L and 4t. Grade Summary al 100% 7 8 9 Attempts remaining: 5 4 5 6 attempt) detailed view Hints: deduction per hint. Hints remaining: Feedback: deduction per feedback. 10% Part (b Express the magnitude of the average emf induced in loop 1,EI, in terms of B, Land v. A 10% Part (c) Calculate the numerical value of E1,in volts. A 10% Part (d) What's the direction of the current induced by EI? 10% Part (e) Express the change of the magnetic flux going through the loop 2,4p2,in terms of B,v, L and 4r. 10% Part (n Express the magnitude of the emf induced in loop 2, E2,in terms of B, Land v. A 10% Part (g) Calculate the numerical value of E2, in volts. 10% Part Calculate the numerical value of in A.

Explanation / Answer

part(a)

let the rod moved a distance dx in time dt with speed v

dx = v*dt

increase in area = L*dx = L*v*dt

magnetic flux phi1 = B*A = B*L*v*dt

============================

part(b)

average induced emf = rate of change in flux

induced emf e1 = B*L*v*dt/dt = B*L*v

=============

part(c)

e1 = 0.75*0.69*0.16 = 0.0828 V

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part(d)

as the rod moves the magnetic flux increases

the magnetic field due to induced current is out of page

the current is directed from B to A throught rod(counterclockwise)

=====================

part(e)

let the rod moved a distance dx in time dt with speed v

dx = v*dt

decrease in area = L*dx = L*v*dt

magnetic flux phi1 = B*A = B*L*v*dt

-------------------------

part(f)

average induced emf = rate of change in flux

induced emf e1 = B*L*v*dt/dt = B*L*v

-------------------
part(g)

e2 = 0.75*0.69*0.16 = 0.0828 V

------------

part(h)

as the rod moves the magnetic flux decreases

the magnetic field due to induced current is into the page

the current is directed from B to A through rod(clockwise)

part(i)

current i = e1/R = B*L*V/R

part(j)

current I = 0.0828/140 = 0.0005914 A

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