A short bar magnet has a magnetic moment of $0.48$ J T$^{-1}$. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of $10$ cm from the centre of the magnet on (a) the axis.

If the solenoid in Exercise 5.5 is free to turn about the vertical direction and a uniform horizontal magnetic field of $0.25$ T is applied, what is the magnitude of torque on the solenoid when its axis makes an angle of $30^{\circ}$ with the direction of applied field?

A bar magnet of magnetic moment $1.5$ J T$^{-1}$ lies aligned with the direction of a uniform magnetic field of $0.22$ T. (a) What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment: (i) normal to the field direction?

A closely wound solenoid of $2000$ turns and area of cross-section $1.6 \times 10^{-4}$ m$^2$, carrying a current of $4.0$ A, is suspended through its centre allowing it to turn in a horizontal plane. (a) What is the magnetic moment associated with the solenoid?

A closely wound solenoid of $2000$ turns and area of cross-section $1.6 \times 10^{-4}$ m$^2$, carrying a current of $4.0$ A, is suspended through its centre allowing it to turn in a horizontal plane. (b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of $7.5 \times 10^{-2}$ T is set up at an angle of $30^{\circ}$ with the axis of the solenoid?

A short bar magnet of magnetic moment $m = 0.32$ JT$^{-1}$ is placed in a uniform magnetic field of $0.15$ T. If the bar is free to rotate in the plane of the field, which orientation would correspond to its (b) unstable equilibrium? What is the potential energy of the magnet in each case?

A short bar magnet of magnetic moment $m = 0.32$ JT$^{-1}$ is placed in a uniform magnetic field of $0.15$ T. If the bar is free to rotate in the plane of the field, which orientation would correspond to its (a) stable equilibrium? What is the potential energy of the magnet in each case?

A bar magnet of magnetic moment $1.5$ J T$^{-1}$ lies aligned with the direction of a uniform magnetic field of $0.22$ T. (a) What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment: (ii) opposite to the field direction?

A bar magnet of magnetic moment $1.5$ J T$^{-1}$ lies aligned with the direction of a uniform magnetic field of $0.22$ T. (b) What is the torque on the magnet in cases (i) and (ii)?

A short bar magnet placed with its axis at $30^{\circ}$ with a uniform external magnetic field of $0.25$ T experiences a torque of magnitude equal to $4.5 \times 10^{-2}$ J. What is the magnitude of magnetic moment of the magnet?

A closely wound solenoid of $800$ turns and area of cross section $2.5 \times 10^{-4}$ m$^2$ carries a current of $3.0$ A. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?

A short bar magnet has a magnetic moment of $0.48$ J T$^{-1}$. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of $10$ cm from the centre of the magnet on (b) the equatorial lines (normal bisector) of the magnet.