A uniform magnetic B^vector perpendicular to a wire loop varies with time as sho

Question

A uniform magnetic B^vector perpendicular to a wire loop varies with time as shown in Fig. 34-20a. Which of the plots in Fig. 34-20b best represents the induced current in the loop as a function of time? A flexible conducting loop is in the shape of a circle with a variable radius. The loop is in a uniform magnetic field perpendicular to the plane of the loop. To sustain a constant emf E in the loop, the radius r must vary with time according to r(t) prop Squareroot t. r(t) prop t. r(t) prop t^2. r should be constant. A flexible wire loop in the shape of a circle has a radius that grows linearly with time. There is a magnetic field perpendicular to the plane of the loop that has a magnitude inversely proportional to the distance from the center of loop. B(r) prop 1/r. How does the emf E vary with time? E prop t^2 E prop t E prop Squareroot t E is constant. The magnetic flux through a wire loop changes by Delta Phi _B in a time Delta t. The change in flux Delta Phi _B is proportional to the current in the wire. the resistance of the wire. the net charge that flows across any cross section in the wire. the potential difference between any two fixed points in the wire.

Explanation / Answer

1 ) emf = d(B*A)/dt

in this case

emf = A *dB/dt

so emf is directly proposal to the slope of this curve

so fig A is correct in first part slope increasing than constant than decreasing than zero

2)

emf = d(B*A)/dt

in this case   

emf = B*dA/dt = B*d(pi*r2) /dt

this to be constant r must proposnal to sqrt(t)

A option is correct

3)

emf = d(B*A)/dt   

r = C1*t

B = C2/r = C2/(C1*t)

emf = d[{C2/(C1*t) }*pi *(C1*t)2 ] /dt

= pi*C1*c2

which is constant D

4) current in wire

because flux = B.A

change in flux is either due to change in B or in Area

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