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A bar magnet is held perpendicular to a uniform magnetic field. If the couple acting on the magnet is to be halved by rotating it, then the angle by which it is to be rotated is
- a)30o
- b)45o
- c)60o
- d)90o
Correct answer is option 'C'. Can you explain this answer?
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A bar magnet is held perpendicular to a uniform magnetic field. If the...
Solution:
Given, couple acting on the magnet is halved by rotating it.
Let's consider the magnetic moment of the bar magnet is M and the magnetic field is B.
The torque acting on the bar magnet is given by:
τ = MBsinθ
where θ is the angle between the magnetic moment and the magnetic field.
If we rotate the bar magnet by an angle θ', then the new angle between the magnetic moment and the magnetic field is (90° - θ').
The new torque acting on the bar magnet is given by:
τ' = MBsin(90° - θ') = MBcosθ'
Now, we need to find the angle θ' such that τ' is half of τ.
So, we have:
MBcosθ' = (1/2)MBsinθ
cosθ' = (1/2)sinθ
tanθ' = (1/2)cotθ = (1/2)tan(90° - θ)
θ' = 60°
Therefore, the angle by which the bar magnet has to be rotated is 60°. Hence, option C is the correct answer.
Given, couple acting on the magnet is halved by rotating it.
Let's consider the magnetic moment of the bar magnet is M and the magnetic field is B.
The torque acting on the bar magnet is given by:
τ = MBsinθ
where θ is the angle between the magnetic moment and the magnetic field.
If we rotate the bar magnet by an angle θ', then the new angle between the magnetic moment and the magnetic field is (90° - θ').
The new torque acting on the bar magnet is given by:
τ' = MBsin(90° - θ') = MBcosθ'
Now, we need to find the angle θ' such that τ' is half of τ.
So, we have:
MBcosθ' = (1/2)MBsinθ
cosθ' = (1/2)sinθ
tanθ' = (1/2)cotθ = (1/2)tan(90° - θ)
θ' = 60°
Therefore, the angle by which the bar magnet has to be rotated is 60°. Hence, option C is the correct answer.
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A bar magnet is held perpendicular to a uniform magnetic field. If the couple acting on the magnet is to be halved by rotating it, then the angle by which it is to be rotated isa)30ob)45oc)60od)90oCorrect answer is option 'C'. Can you explain this answer?
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