A conductor of length 5 m moves at an angle 30° to the direction of the magnetic field of flux density 1.4 wb/m2. If the velocity of the conductor is 40 m/s, then calculate the EMF induced in it.

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SSC JE Electrical 05 Jun 2024 Shift 3 Official Paper - 1
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  1. 140 volts
  2. 0 volt
  3. 1400 volts
  4. 100 volts

Answer (Detailed Solution Below)

Option 1 : 140 volts
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Detailed Solution

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Concept of Induced EMF in a Moving Conductor:

The EMF (E) induced in a conductor moving in a magnetic field is given by the formula:

E = B × L × v × sin(θ)

Where,

  • B = Magnetic Flux Density (in Wb/m2)
  • L = Length of the Conductor (in meters)
  • v = Velocity of the Conductor (in m/s)
  • θ = Angle between the direction of motion and the magnetic field

Given Data:

  • B = 1.4 Wb/m2
  • L = 5 m
  • v = 40 m/s
  • θ = 30°

Calculation:

First, convert the angle θ to radians (if necessary). However, in this case, we can use degrees directly with the sine function:

sin(30°) = 0.5

Using the formula:

E = B × L × v × sin(θ)

E = 1.4 Wb/m2 × 5 m × 40 m/s × 0.5

E = 1.4 × 5 × 40 × 0.5

E = 1.4 × 100

E = 140 V

Conclusion:

Hence, the EMF induced in the conductor is 140 V.

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