PREPARED BY:
Dr P.K. SHARMA PGT(Phy) JNV- Kokrajhar
TORQUE ON A BAR MAGNET WHEN PLACED IN UNIFORM
MAGNETIC FIELD
TORQUE ON A BAR MAGNET WHEN PLACED IN UNIFORM MAGNETIC FIELD
Uniform Magnetic field Bar Magnet Placed In Uniform Magnetic Field Expression For Torque Direction Of Torque Special Cases Definition Of Magnetic Dipole Moment Potential Energy Evaluation Home Work
.
1. To know about uniform magnetic field.
2. To understand the cause of torque acting
on a bar magnet when placed in uniform
magnetic field.
3. To know about P. E. in stable & unstable
equilibrium.
4.To find direction of torque.
5. To solve numerical problems based on Torque & P.E.Contd…
PREVIOUS KNOWLEDGE
1.Define uniform magnetic field .
2. Define magnetic dipole moment of a bar magnet.
3. What do you mean by a couple of forces?
4. Can a couple of forces constitute a torque?
5. What is the formula of torque?back
The region in which the magnitude and the direction of magnetic field is the same at each point
CONTD…
CONTD…
B
BAR MAGNET PLACED IN UNIFORM MAGNETIC FIELD
B
mqS
mq BN
l2
K
Torque = Force x Perpendicular Distance
Contd..
= qm B X K N
In ∆ SNK
Sinθ = NK/2l
NK = 2l Sinθ
Therefore, = qm B x 2l Sinθ
= (qm x 2l )B Sinθ
=M B Sinθ
Case-(i): When θ =00(Stable Equilibrium),
=0
Case-(ii): When θ=900
=MB
Case-(iii): When θ =1800(Unstable Equilibrium),
=0
Thus, torque acting on the bar magnet is max, when it is placed perpendicular to the magnetic field. CONTD..
In vector form,=M x B
θ
M
B
=M x B=M x B
DEFINITION OF DIPOLE MOMENT
CONTD…
=M B Sinθ
When, θ=900 & B=1,then M=
Thus, magnetic dipole moment may be definedas the torque acting on a magnetic dipole placedperpendicular to a uniform magnetic field of unitstrength. S.I. unit of magnetic dipole moment is J/T.
EXPRESSION FOR WORK DONE OR POTENTIAL ENERGY
CONTD…
Work done in rotating the dipole through a small angle dθ,dw = dθ = MB Sinθdθ
If the dipole is rotated from θ = θ1 to θ = θ2 ,total work done,
W =
=- MB (cos θ2 – cos θ1) If θ1=900 & θ2 =θ0,then W = - MB cos θ This work done is stored in the form of Potential Energy i.e. U = - MB cos θ
2
1
dMBSin
Case-(i): When θ =00(Stable Equilibrium),
= - MB
Case-(ii): When θ=900
= 0
Case-(iii): When θ =1800(Unstable Equilibrium),
= MB
Thus, the P. E. of the bar magnet is max, when it is placed antiparallel to the magnetic field.
CONTD..
U
U
U
EVALUATION
Q1. When is the torque acting on the bar magnet
maximum?
Q2. What is the condition of stable equilibrium?
Q3. A magnetic needle of magnetic moment
4.8 x 10 -2 JT-1 is placed at 300 with
the direction of magnetic field of magnitude
3x10-2 T. What is the torque acting theneedle? CONTD…
ASSIGNMENT
Q1. Define uniform magnetic field.
Q2. Derive an expression for torque acting on bar magnet when placed
at an angle θ with the direction of uniform magnetic field.
Q3. A short bar magnet placed with its axis at 300 with a uniform
magnetic field of o.16T experiences a torque of 0.032J.
(a) Estimate the magnetic moment of the magnet.
(b) If the bar were free to rotate, which orientation would
correspond to its (i) stable (ii) unstable equilibrium?
What is the potential energy in case (i) & (ii)?
CONTD…
THANK YOU
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