A current carrying loop is placed in a uniform magnetic field in four different orientations I, II, III and IV as shown in figure. Arrange them in decreasing order of potential energy
l > lll> ll > lV
l > ll > lll > lV
l > lV > ll > lll
lll > lV > l > ll
C.
l > lV > ll > lll
As we know that, potential energy of a magnet in a magnetic field.
U = - m .B
where, m = magnetic dipole moment of the magnet
B = magnetic field
Case l :- θ = 180o
U1 = mB. cos 180o
= mB [ cos 180o = -1 ]
Case ll :- θ = 90o
U2 = 0 [ cos 90o = 0 ]
Case lll :- θ is acute angle
θ ∈ ( 0o, 90o )
∴ cosθ = positive
Thus U3 = negative
Case lV:- θ is obtuse
θ ∈ ( 90o, 180o )
∴ cos ∈ ( 0, -1 )
Thus, U4 = positive
Therefore, decreasing order of PE is
l > lV > ll > lll
