write tha expression for tha torque on a magnetic dipole and explain the terms
Answers
Answer:
Plane of the loop i at an angle with the direction of the magnetic field. Let θ be the angle between normal and the field. The forces on BC and DA are equal and opposite and they cancel each other.
Force on AB is F
1
and the force on CD is F
2
F
1
=F
2
=IbB
Magnitude of the torque is shown in the figure
τ=F
1
2
a
sinθ+F
2
2
a
sinθ
=IbB
2
a
sinθ+IbB
2
a
sinθ
=I(ab)Bsinθ
=IABsinθ ; where A=ab
If there are 'n' such turns then there torque will be nIABsinθ
Magnetic moment of the current, m=IA
τ
=
m
×
B
b) Principle: MCG is based on the principle that a current carrying coil placed in uniform magnetic field experiences a torque.
Construction:
The galvanometer consists of a coil, with many turns, free to rotate about a fixed axis (Fig. b), in a uniform radial magnetic field. There is a cylindrical soft iron core which not only makes the field radial but also increases the strength of the magnetic field. When a current flows through the coil, a torque acts on it.
Working: torque acting on the coil is given by:
τ=NIAB
Since the field is radial by design, we have taken sinθ=1 in the above expression for the torque.
The magnetic torque NIAB tends to rotate the coil. A spring Sp provides a counter torque kφ that balances the magnetic torque NIAB; resulting in a steady angular deflection φ. In equilibrium,
kφ=NIAB
where k is the torsional constant of the spring; i.e. the restoring torque per unit twist. The deflection φ is indicated on the scale by a pointer attached to the spring.
ϕ=
k
NABI
