The magnetic field at a point situated 10 cm from a magnetic dipole is observed to be 2.0 × 10^ -4 T . Calculate the magnetic moment of the dipole if this point is located in the end-on position.

Correct answer: B. 1.0 A m^2 The magnetic field at the end-on (axial) position of a short magnetic dipole is given by: B = (μ_0)/(4π) (2M)/(r^3) Given B = 2.0 × 10^ -4 T and r = 10 cm = 0.1 m . Substituting the values into the formula: 2.0 × 10^ -4 = 10^ -7 × (2M)/((0.1)^3) 2.0 × 10^ -4 = 10^ -7 × 2M 10^ -3 2.0 × 10^ -4 = 10^ -4 × 2M 2M = 2.0 M = 1.0 A m^2

Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Permanent Magnets

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Permanent Magnets

The magnetic field at a point situated 10 cm from a magnetic dipole...

The magnetic field at a point situated

10 \text{ cm}

from a magnetic dipole is observed to be

2.0 \times 10^{-4} \text{ T}

. Calculate the magnetic moment of the dipole if this point is located in the end-on position.

Options

A $4.0 \text{ A m}^2$
B $1.0 \text{ A m}^2$
C $0.5 \text{ A m}^2$
D $2.0 \text{ A m}^2$

Correct answer

B. $1.0 \text{ A m}^2$

Step-by-step solution

The magnetic field at the end-on (axial) position of a short magnetic dipole is given by:

B = \dfrac{\mu_0}{4\pi} \dfrac{2M}{r^3}

Given

B = 2.0 \times 10^{-4} \text{ T}

and

r = 10 \text{ cm} = 0.1 \text{ m}

.

Substituting the values into the formula:

2.0 \times 10^{-4} = 10^{-7} \times \dfrac{2M}{(0.1)^3}

2.0 \times 10^{-4} = 10^{-7} \times \dfrac{2M}{10^{-3}}

2.0 \times 10^{-4} = 10^{-4} \times 2M

2M = 2.0

M = 1.0 \text{ A m}^2

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