A magnetic field, directed along the ( z )-axis, varies with time ( T ) as shown in – [Free] B112

A magnetic field, directed along the ( z )-axis, varies with time ( T ) as shown in the figure. A planar conducting loop is in the magnetic field. The magnetic field is perpendicular to the plane of the loop. Select the appropriate description for the magnitude of the EMF induced in the loop (EMF-mag) and for its direction (EMF-dir) at the indicated times. Select a response for each statement. The EMF-mag at C is equal to zero. The EMF-dir at G is the same as at F. The EMF-mag at J is … that at G . The EMF-mag at H is … that at D . The EMF-mag at D is … that at G. The EMF-mag at J is … that at A . The EMF-dir at L is opposite to that at G. The induced EMF in a loop is related to the rate of change of the magnetic flux through the loop, and its direction is given by Lenz’s Law.

Answer

Understanding Induced EMF and Faraday’s Law

Induced EMF is the voltage generated in a coil due to a change in magnetic flux through it. It occurs when either:

• The coil moves through a magnetic field
• The magnetic field around the coil changes

Faraday’s Law

EMF = -N (dϕ/dT)

Where:
T → Time
N → Number of coil turns

Magnetic Flux Formula

ϕ = ∫ B · dA

Where:
B → Magnetic field
dA → Small cross-sectional area

Therefore:

EMF ∝ dB/dT

EMF is proportional to the slope of the Magnetic Field vs Time (B-T) graph.

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Analysis of EMF Based on Slope

1. The EMF-magnitude at C is equal to zero: False
   The slope at point C is not zero (it’s negative), so EMF is not zero.
2. The EMF-direction at G is the same as at F: True
   Both G and F have positive slopes of equal magnitude, so the EMF direction is the same.
3. The EMF-magnitude at J is ____ that at G: Less than
   G has a steeper slope than J, hence greater EMF.
4. The EMF-magnitude at H is ____ that at D: Greater than
   H has a steeper slope than D, so the EMF at H is stronger.
5. The EMF-magnitude at D is ____ that at G: Equal to
   The slopes are equal, so EMF magnitudes are equal.
6. The EMF-magnitude at J is ____ that at A: Greater than
   A has zero slope → EMF = 0. J has a positive slope → EMF > 0.
7. The EMF-direction at L is opposite to that at G: True
   L has a negative slope, G has a positive slope. So, the direction is opposite.

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Answer Summary

• 1. False
• 2. True
• 3. Less than
• 4. Greater than
• 5. Equal to
• 6. Greater than
• 7. True