A conductor of length 0.5m moves in a uniform magnetic field of flux density 2 wbm^2. at a uniform velocity of 40m/s. Calculate the induced EMF under the following conditions:
(1) the conductor moves at right angle to the magnetic field
(2) the conductor moves at an angle of 30 degrees to the direction of the field
To calculate the induced electromotive force (EMF) in the conductor, you can use Faraday's Law of Electromagnetic Induction. The formula for finding the induced EMF is:
EMF = B * L * v * sin(theta)
Where:
- B is the flux density of the magnetic field.
- L is the length of the conductor.
- v is the velocity of the conductor.
- theta is the angle between the velocity vector and the magnetic field vector.
(1) When the conductor moves at a right angle to the magnetic field:
- B = 2 Wb/m²
- L = 0.5 m
- v = 40 m/s
- theta = 90°
Now we can plug these values into the formula to calculate the induced EMF:
EMF = 2 Wb/m² * 0.5 m * 40 m/s * sin(90°) = 40 V
Therefore, the induced EMF when the conductor moves at a right angle to the magnetic field is 40 volts.
(2) When the conductor moves at an angle of 30 degrees to the direction of the field:
- B = 2 Wb/m²
- L = 0.5 m
- v = 40 m/s
- theta = 30°
Plug these values into the formula:
EMF = 2 Wb/m² * 0.5 m * 40 m/s * sin(30°) = 20 V
Therefore, the induced EMF when the conductor moves at an angle of 30 degrees to the direction of the field is 20 volts.