Description: Exercise 29.38 An elastic circular conducting loop expands at a con
ID: 2298209 • Letter: D
Question
Description: Exercise 29.38
An elastic circular conducting loop expands at a constant rate over time such that its radius is given by r(t)=r0+vt, where r0=0.251m and v=0.0253m/s. The loop has a constant resistance of R=10.5? and is placed in a uniform magnetic field of magnitude B0=0.901T, perpendicular to the plane of the loop, as shown in the figure.
Calculate the direction and the magnitude of the induced current, i, at t=5.53s.
Please include a multiplication sign (*) to indicate that two units are being multiplied.
i=[Num] [Units],
flowing (Click For List)counterclockwiseclockwise through the loop.
An elastic circular conducting loop expands at a constant rate over time such that its radius is given by r(t)=r0+vt, where r0=0.251m and v=0.0253m/s. The loop has a constant resistance of R=10.5? and is placed in a uniform magnetic field of magnitude B0=0.901T, perpendicular to the plane of the loop, as shown in the figure.
Calculate the direction and the magnitude of the induced current, i, at t=5.53s.
Please include a multiplication sign (*) to indicate that two units are being multiplied.
i=[Num] [Units],
flowing (Click For List)counterclockwiseclockwise through the loop.
Explanation / Answer
dA/dt
=(pi*r^2)/dt
=2pi*r*dr/dt
= 2*pi*(0.251+0.0253*t)*0.0253
emf = NBdA/dt
=0.901*2*pi*(0.251+0.0253*5.53)*0.0253
=0.056 volt
current = volt/resistance
= 0.056/10.5
=5.3322*10^-3 A
direction clockwise