A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60º, and one of the fields has a magnitude of 1.2 x 10-2T. If the dipole comes to stable equilibrium at an angle of 15º with this field, what is the magnitude of the other field?
Magnitude of one of the magnetic fields, B1= 1.2 × 10 - 2 T
Magnitude of the other magnetic field = B2
Angle between the two fields, θ= 60°
At stable equilibrium, the angle between the dipole and field B1, θ1= 15°
Angle between the dipole and field B2, θ2= θ - θ1 = 60° - 15° = 45°
At rotational equilibrium, the torques between both the fields must balance each other.
∴Torque due to field B1= Torque due to field B2
MB1sinθ1= MB2sinθ2
Where, M= Magnetic moment of the dipole
Hence, the magnitude of the other magnetic field is 4.39 × 10 - 3T.
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A closely wound solenoid of 800 turns and area of cross section 2.5 × 10−4 m2 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?
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(b) What is the torque on the magnet in cases (i) and (ii)?
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(b) Obtain the displacement current across the plates.
(c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.
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(b) It is necessary to use satellites for long distance TV transmission. Why?
(c) Optical and radio telescopes are built on the ground but X-ray astronomy is possible only from satellites orbiting the earth. Why?
(d) The small ozone layer on top of the stratosphere is crucial for human survival. Why?
(e) If the earth did not have an atmosphere, would its average surface temperature be higher or lower than what it is now?
(f) Some scientists have predicted that a global nuclear war on the earth would be followed by a severe ‘nuclear winter’ with a devastating effect on life on earth. What might be the basis of this prediction?
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Which among the curves shown in Fig. 1.35 cannot possibly represent electrostatic field lines?
(a)
(b)
(c)
(d)
(e)