Calculating Induced Voltage in a Rotating Rectangular Loop with Magnetic Field

[lazyaditya]

Q. A 30 cm by 40 cm rectangular loop rotates at 130 rad/sec in a magnetic field 0.06Wb/metre sqre normal to the axis of rotation. If the loop has 50 turns, determine the induced voltage in the loop ?

Attempt !

V(induced) in 1 turn = ∫(u X B).dS

my vector u will be ρω in a∅ direction but i am unable to understand the direction of magnetic field what does it mean by direction perpendicular to axis of rotation ?

 

[berkeman]

Q. A 30 cm by 40 cm rectangular loop rotates at 130 rad/sec in a magnetic field 0.06Wb/metre sqre normal to the axis of rotation. If the loop has 50 turns, determine the induced voltage in the loop ?

Attempt !

V(induced) in 1 turn = ∫(u X B).dS

my vector u will be ρω in a∅ direction but i am unable to understand the direction of magnetic field what does it mean by direction perpendicular to axis of rotation ?

It means that the magnetic field goes straight through the loop. Say that the loop's axis of rotation is the x direction, then the magnetic field could be in the y or z direction.

 

[rude man]

Q. A 30 cm by 40 cm rectangular loop rotates at 130 rad/sec in a magnetic field 0.06Wb/metre sqre normal to the axis of rotation. If the loop has 50 turns, determine the induced voltage in the loop ?

Attempt !

V(induced) in 1 turn = ∫(u X B).dS

my vector u will be ρω in a∅ direction but i am unable to understand the direction of magnetic field what does it mean by direction perpendicular to axis of rotation ?

I think it would be easier to use Farady's law of induction which equates emf to rate of change of magnetic flux.

 

[lazyaditya]

It means that the magnetic field goes straight through the loop. Say that the loop's axis of rotation is the x direction, then the magnetic field could be in the y or z direction.

but then if i am considering the direction of rotation to be A∅ wouldn't both the directions Aρ
and Az will be perpendicular to it !

 

[lazyaditya]

I think it would be easier to use Farady's law of induction which equates emf to rate of change of magnetic flux.

how should i use faraday law in this the conductor position is changing ! wouldn't the faraday law equation result in the equation i have used in the end !

 

[rude man]

how should i use faraday law in this the conductor position is changing ! wouldn't the faraday law equation result in the equation i have used in the end !

Yes, the conductor position is changing. That's what makes the magnetic flux change, since flux = B dot area where B and area are vectors ...

Yes, yopur equation is tantamount to farady's law. i just meant that using flux = B x A is easier ...