TORQUE ON A BAR MAGNET WHEN PLACED IN

TORQUE ON A BAR MAGNET WHEN PLACED IN UNIFORM MAGNETIC FIELD PREPARED BY: Dr P. K. SHARMA PGT(Phy) JNV- Kokrajhar

TORQUE ON A BAR MAGNET WHEN PLACED IN UNIFORM MAGNETIC FIELD n n n n n 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 3. on a bar magnet when placed in uniform 4. magnetic field. 5. 3. To know about P. E. in stable & unstable 6. equilibrium. 7. 4. To find direction of torque. 8. 5. To solve numerical problems based on Torque & P. E. Contd…

PREVIOUS KNOWLEDGE 1. Define uniform magnetic field. 2. 2. Define magnetic dipole moment of a bar magnet. 3. 3. What do you mean by a couple of forces? 4. 4. Can a couple of forces constitute a torque? 5. 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…

BAR MAGNET PLACED IN UNIFORM MAGNETIC FIELD CONTD…

Torque = Force x Perpendicular Distance = qm B X K N In ∆ SNK Sinθ = NK/2 l NK = 2 l Sinθ Therefore, = qm B x 2 l Sinθ = (qm x 2 l )B Sinθ =M B Sinθ Contd. .

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 CONTD. . magnetic field.

In vector form, =M x B M θ =M x B B

DEFINITION OF DIPOLE MOMENT =M B Sinθ When, θ=900 & B=1, then M= Thus, magnetic dipole moment may be defined as the torque acting on a magnetic dipole placed perpendicular to a uniform magnetic field of unit strength. S. I. unit of magnetic dipole moment is J/T. CONTD…

EXPRESSION FOR WORK DONE OR POTENTIAL ENERGY Work done in rotating the dipole through a small angle dθ, dw = dθ = MB Sinθdθ If the dipole is rotated from θ = θ 1 to θ = θ 2 , total work done, W= =- MB (cos θ 2 – cos θ 1) If θ 1=900 & θ 2 =θ 0, then W = - MB cos θ This work done is stored in the form of Potential Energy i. e. U = - MB cos θ CONTD…

Case-(i): When θ =00(Stable Equilibrium), U = - MB Case-(ii): When θ=900 U=0 Case-(iii): When θ =1800(Unstable Equilibrium), U = MB Thus, the P. E. of the bar magnet is max, when it is placed antiparallel to the magnetic field. CONTD. .

EVALUATION Q 1. When is the torque acting on the bar magnet maximum? Q 2. What is the condition of stable equilibrium? Q 3. 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 3 x 10 -2 T. What is the torque acting theneedle? CONTD…

ASSIGNMENT Q 1. Define uniform magnetic field. Q 2. Derive an expression for torque acting on bar magnet when placed at an angle θ with the direction of uniform magnetic field. Q 3. A short bar magnet placed with its axis at 300 with a uniform magnetic field of o. 16 T experiences a torque of 0. 032 J. (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…

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