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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 Am
^{2}. **Given:**Distance from centre = r = 10 cm = 0.1 m, Magnetic moment = 0.2 Am^{2}. 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 Am
^{2}. **Given:**Distance from centre = r = 20 cm = 0.2 m, Magnetic moment = 5 Am^{2}.- 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 Am
^{2}. **Given:**Distance from either pole = 0.5 m, Magnetic moment = 5 Am^{2}.**To Find:**Magnetic induction= B = ?**Solution:**

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

∴ r^{2} + l^{2} = (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 Am
^{2}. **Given:**Distance from centre = r = 10 cm = 0.1 m, Magnetic moment = 0.25 Am^{2}.**To Find:**Magnetic induction B_{axis}= ? and B_{equator}= ?**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 = 2*l*= 5 cm = 0.05 m**To Find:**Magnetic induction= B = ?**Solution:**

Magnetic Moment = M = m . 2*l* = 10 x 0.05 = 0.5 Am^{2}

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

∴ r^{2} + l^{2} = (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 Am
^{2}. **Given:**Distance from centre = r = 20 cm = 0.2 m, Magnetic moment = 0.5 Am^{2}.**To Find:**Magnetic induction B_{axis}= ? and B_{equator}= ?**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 Am
^{2}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 Am^{2}, 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, μ_{o}/4π = 10^{-7}Wb/Am.**To Find:**Magnetic induction = B_{axis}= ?**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/m^{2}. 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/m^{2}^{, }Point on equator.**To Find:**Magnetic moment = M = ?**Solution:**

**Ans:** The magnetic moment is 0.5 Am^{2}

#### 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/m^{2}. 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 = B_{axis}= 1.5 x 10^{-5}Wb/m^{2},**To Find:**B_{equator}= ?**Solution:**

**Ans:** Magnetic induction at a point on equator is 7.5 x 10^{-6} Wb/m^{2}.

#### 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/m^{2}. 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/m^{2}^{, }Point on axis.**To Find:**Magnetic moment = M = ?**Solution:**

**Ans:** The magnetic moment is 0.2 Am^{2}

#### 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:**B_{axis}= B_{equator},**To Find:**ratio of distances r_{P}:r_{Q}= ?**Solution:**

**Ans:** The required ratio of distances is 2^{1/3 }: 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/m^{2}, 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/m^{2}, Point on Equator, distance from centre = r = 6400 km = 6.4 x 10^{6}m**To Find:**Magnetic moment = M = ?, Magnetic field at north pole = ?**Solution:**

**Ans:** The magnetic moment of magnet is 7.86 x 10^{22} Am^{2}

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, μ_{o}/4π = 10^{-7}Wb/Am.**To Find:**Magnetic induction = B_{axis}= ?**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 M
_{1}= 2.7 Am^{2}and M_{2}= 3.2 Am^{2}respectively are kept as shown. Find the resultant magnetic field due to the magnets at P. r_{1}= 30 cm and r_{2}= 40 cm.

**Given:**M_{1}= 2.7 Am^{2}, M_{2}= 3.2 Am^{2}, r_{1}= 30 cm = 0.3 m, and r_{2}= 40 cm = 0.4 m.

Science > Physics > Magnetism >You are Here |

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Chemistry |
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Mathematics |