2) Induced EMF and Current in a Shrinking Loop Shrinking Loop. A circular loop o

Question

2) Induced EMF and Current in a Shrinking Loop

Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 165 cm , but its circumference is decreasing at a constant rate of 11.0 cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 1.00 T , which is oriented perpendicular to the plane of the loop. Assume that you are facing the loop and that the magnetic field points into the loop.

Part A

Find the magnitude of the emf E induced in the loop after exactly time 6.00 s has passed since the circumference of the loop started to decrease (In volts).

Part B

Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field (clockwise or counter-clockwise).

Explanation / Answer

Circumference C= 2r
Rate of change of circumference is
dC/dt = 2 dr /dt = - 0.11m/s ( GIVEN)
Minus sign to denote the decrease in value.
--------------------------------------...
A = r^2
The rate of change of area
dA/dt = 2r dr /dt = - 0.11*r (Replacing 2 dr /dt by -0.14)
--------------------------------------...
Initial circumference = 1.65 m
In 2 second the C decreases by 6*0.11 = 0.66 m
The radius after 2 s is [1.65 - 0.66] / (2) = 0.1575 m
--------------------------------------...
e = - d/dt {BA cos ]
e = - 1* dA/dt since cos = 1 and B = 0.1
e = - 1 *dA/dt
e = 1 *[0.14*r] (Substituting for dA/dt as - 0.11*r)
e = 1 *0.11*0.1575 (Substituting the value of r)
e = 0.01732 V = 17.3mV

clockwise, Since the area of the loop is decreasing, the flux is decreasing; hence, the induced current acts to increase the flux (per Lenz's law). Looking along the field into the loop and utilizing the right hand rule

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.