Hi Guys,
Just have a quick question. Why wouldn't (i) increase the rate of rotation? The answer says only (ii) and (iii) would increase the rate of rotation. Isn't torque equal to 2 x nBIL x r where r is the distance between one of the sides(either KL or JM) of the loop and the axis XY?
By increasing area, wouldn't r increase from 1cm to 2 cm and thus, increase rate of rotation? Also, is the rate of rotation about the torque or something else like frequency?
Thanks. All help will be much appreciated.
If you look at the coil in the image, the area is a 4 x 2. If you change it to a 4 x 4, sides LM and KJ will increase by 2.
For now let's consider the amount of force acting on JUST side LM. We will have
Now theta is just the angle between LM and the Magnetic field which acts on LM. If we look at the image LM is parallel to the Magnetic field so in that position it will never experience a force, which means the torque will always be zero for LM no matter how much we increase it's length (for that one position).
Now let's consider the force on it as it rotates. If we look at LM after half a rotation, it will be perpendicular to the magnetic field which means the force acting on it will be
However the direction of this force is going to be into or out of the page depending on which way the current is flowing. This means the force acting on LM is PARALLEL to the axis of rotation. Now the formula for torque is given by
where
alpha is the angle between the force acting on LM and the Axis of rotation. However we just found out that in this case the force acting on LM is parallel to the axis of rotation. This means alpha = 0 !. Hence the torque is ZERO. So no matter at what time during it's rotation, sides LM and KJ will experience zero force and hence zero torque. For the position in the image the force is zero and hence no torque, and when it's rotating the force will act parallel to the axis of rotation, which means the torque on LM and KJ will be zero. NOTE: The torque is zero but a force still acts, however remember torque also depends on the angle between the Force and the Axis of rotation which allows for Torque to be zero even though the Force is not zero.
All the force does for LM and KJ is essentially 'stretch' the two sides out, so it doesn't matter how much you increase their length by, they will never experience a torque.