Magnetic Induction at a Point on Axis and Equator of a Bar Magnet

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Example – 01:

  • Find the magnetic induction at a point distant 10 cm on the axis of a short bar magnet of moment 0.2 Am2.
  • Given: Distance from centre = r = 10 cm = 0.1 m, Magnetic moment = 0.2 Am2. Point on axis.
  • To Find: Magnetic induction= B = ?
  • Solution:

Ans: The magnetic induction at the point is 4 x 10-5 T

Example – 02:

  • Find the magnetic induction at a point distant 20 cm on the equator of a short bar magnet of moment 5 Am2.
  • Given: Distance from centre = r = 20 cm = 0.2 m, Magnetic moment = 5 Am2.
  • Point on equator.
  • To Find: Magnetic induction= B = ?
  • Solution:



Ans: The magnetic induction at the point is 6.25 x 10-5 T

Example – 03:

  • Find the magnetic induction at a point 0.5 m from either pole on the equator of a bar magnet of moment 5 Am2.
  • Given: Distance from either pole = 0.5 m, Magnetic moment = 5 Am2.
  • To Find: Magnetic induction= B = ?
  • Solution:

As the point is equidistant from either poles it is on equator of the bar magnet

∴  r2 + l2 = (0.5)2 = 0.25



Ans: The magnetic induction at the point is 4 x 10-6 T

Example – 04:

  • Find magnetic induction due to a short bar magnet at a point distant 10 cm a) on its axis and b) on its equator, given that the magnetic dipole moment of the magnet is 0.25 Am2.
  • Given: Distance from centre = r  = 10 cm = 0.1 m, Magnetic moment = 0.25 Am2.
  • To Find: Magnetic induction  Baxis = ? and Bequator = ?
  • Solution:

Ans: The magnetic induction at the point on axis is 5 x 10-5 T and that on equator is 2.5 x 10-5 T

Example – 05:

  • A bar magnet has pole strength 10 Am and a magnetic length of 5 cm. Find the magnetic induction at equidistant point of 10 cm from either pole.
  • Given: Distance from either pole = 10 cm = 0.1 m, pole strength = m = 10 Am, magnetic length = 2l = 5 cm = 0.05 m
  • To Find: Magnetic induction= B = ?
  • Solution:

Magnetic Moment = M = m . 2l = 10 x 0.05 = 0.5 Am2



As the point is equidistant from either poles it is on equator of the bar magnet

∴  r2 + l2 = (0.1)2 = 0.01

Ans: The magnetic induction at the point is 5 x 10-6 T

Example – 06:

  • Find magnetic induction due to a short bar magnet at a point distant 20 cm a) on its axis and b) on its equator, given that the magnetic dipole moment of the magnet is 0.5 Am2.
  • Given: Distance from centre = r  = 20 cm = 0.2 m, Magnetic moment = 0.5 Am2.
  • To Find: Magnetic induction  Baxis = ? and Bequator = ?
  • Solution:



Ans: The magnetic induction at the point on axis is 1.25 x 10-5 T and that on equator is 6.25 x 10-6 T

Example – 07:

  • Find the magnetic induction at a point distant 8 cm on the equator from the centre of a short bar magnet of moment 0.2 JT-1.
  • Given: Distance from centre = r = 8 cm = 0.08 m, Magnetic moment = 0.2 JT-1, Point on equator.
  • To Find: Magnetic induction= B = ?
  • Solution:

Ans: The magnetic induction at the point is 3.91 x 10-5 T

Example – 08:

  • Find the magnetic induction at a point distant 10 cm from the centre of the magnet on the axis of a short bar magnet of moment 0.24 JT-1.
  • Given: Distance from centre = r = 10 cm = 0.1 m, Magnetic moment = 0.24 JT-1. Point on axis.
  • To Find: Magnetic induction= B = ?
  • Solution:



Ans: The magnetic induction at the point is 4.8 x 10-5 T

Example – 09:

  • Find the magnetic induction due to a bar magnet of magnetic induction 0.5 Am2 at a point on its axis at a distance of 15 cm from the nearest pole. The magnetic length of magnet is 10 cm.
  • Given: Magnetic moment = M = 0.5 Am2, distance from nearest pole = 15 cm = 0.15 m, magnetic length = 2 l = 10 cm, l = 5 cm = 0.05 m, distance of point from centre = r = 0.15 + 0.05 = 0.20 m,  μo/4π = 10-7 Wb/Am.
  • To Find: Magnetic induction = Baxis = ?
  • Solution:

Ans: The magnetic induction at the point is 1.422 x 10-5 T

Example – 10:

  • The magnetic induction at a point on equator of a magnetic dipole at a distance of 10 cm from its centre is 5 x 10-5 Wb/m2. Calculate the magnetic moment of the magnet.
  • Given: Distance from centre = r = 10 cm = 0.1 m, Magnetic moment = B = 5 x 10-5 Wb/m2Point on equator.
  • To Find: Magnetic moment = M = ?
  • Solution:



Ans: The magnetic moment is 0.5 Am2

Example – 11:

  • The magnetic induction at a point on the axis at a distance 20 cm from the centre of the magnet is 1.5 x 10-5 Wb/m2. Find the magnetic induction at a point on the equator at the same distance from the centre.
  • Given: distance of point from centre of magnet = r = 20 cm for both the points. Magnetic induction = Baxis =  1.5 x 10-5 Wb/m2,
  • To Find: Bequator = ?
  • Solution:

Ans: Magnetic induction at a point on equator is 7.5 x 10-6 Wb/m2.

Example – 10:

  • The magnetic induction at a point on axis of a magnetic dipole at a distance of 10 cm from its centre is 4 x 10-5 Wb/m2. Calculate the magnetic moment of the magnet.
  • Given: Distance from centre = r = 10 cm = 0.1 m, Magnetic moment = B = 4 x 10-5 Wb/m2Point on axis.
  • To Find: Magnetic moment = M = ?
  • Solution:

Ans: The magnetic moment is 0.2 Am2

Example – 11:

  • The magnetic induction at point P on the axis of short bar magnet is equal to the magnetic induction at point Q on the equatorial line. Find the ratio of the distances from the centre of magnet.
  • Given: Baxis = Bequator,
  • To Find: ratio of distances rP:rQ = ?
  • Solution:



Ans: The required ratio of distances is 21/3 : 1

Example – 12:

  • Earth’s magnetic field may be imagined to be due to a magnetic dipole located at the centre of the earth. If the magnetic field at a point on the magnetic equator is 3 x 10-5 Wb/m2, What is the magnetic moment of such a magnet? What is the value of earth’s magnetic field at the north pole of the earth? Radius of the earth = 6400 Km.
  • Given: B = 3 x 10-5 Wb/m2, Point on Equator, distance from centre = r = 6400 km = 6.4 x 106 m
  • To Find: Magnetic moment = M = ?, Magnetic field at north pole = ?
  • Solution:

Equator

Ans: The magnetic moment of magnet is 7.86 x 1022 Am2



and magnetic induction at north pole is 6 x 10-5 T.

Example – 13:

  • A magnet has magnetic length 0.10 m and pole strength 12 Am. Find the magnitude of the magnetic field B at a point on its axis at a distance of 0,02 m from centre.
  • Given: Magnetic length = 2l = 0.10 m, l = 0.05 m, pole strength = 12 Am, distance from the centre = r = 0.02 m, μo/4π = 10-7 Wb/Am.
  • To Find: Magnetic induction = Baxis = ?
  • Solution:

Ans: Magnetic induction on the axis is 3.4 x 10-5 T.

Example – 13:

  • Two short magnets A and B of magnetic moments M1 = 2.7 Am2 and M2 = 3.2 Am2 respectively are kept as shown. Find the resultant magnetic field due to the magnets at P. r1 = 30 cm and r2 = 40 cm.

  • Given: M1 = 2.7 Am2, M2 = 3.2 Am2, r1 = 30 cm = 0.3 m, and r2 = 40 cm = 0.4 m.

 

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