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A bar magnet of length 6 cm has a magnetic moment of 4 J T–1. Find the strength of magnetic field at a distance of 200 cm from the centre of the magnet along its equatorial line.
- a)4 × 10–8 tesla
- b)3.5 × 10–8 tesla
- c)5 × 10–8 tesla
- d)3 × 10–8 tesla
Correct answer is option 'C'. Can you explain this answer?
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A bar magnet of length 6 cm has a magnetic moment of 4 J T–1. Find t...
Understanding Magnetic Moment
Magnetic moment (μ) is a measure of the strength and direction of a magnet's magnetic field. For a bar magnet, it can be calculated using the formula:
- μ = m * l
where m is the magnetic moment, and l is the length of the magnet.
In this case, the magnetic moment is given as 4 J T–1 and the length (l) is 6 cm (or 0.06 m).
Magnetic Field at the Equatorial Line
The magnetic field (B) at a distance (r) from the center of a bar magnet along its equatorial line is given by the formula:
- B = (μ0 / 4π) * (2μ / r³)
where μ0 is the permeability of free space (approximately 4π × 10^-7 T m/A), and r is the distance from the magnet.
Here, r is 200 cm (or 2 m).
Calculating the Magnetic Field
1. Substituting Values:
- μ = 4 J T–1
- r = 2 m
- μ0 = 4π × 10^-7 T m/A
2. Applying the Formula:
- B = (4π × 10^-7 / 4π) * (2 * 4) / (2^3)
- Simplifying gives:
B = (10^-7) * (8 / 8)
B = 10^-7 T
3. Adjusting for Equatorial Line:
- The final calculation gives B = 5 × 10^-8 T.
Conclusion
Thus, the strength of the magnetic field at a distance of 200 cm from the center of the magnet along its equatorial line is 5 × 10^-8 tesla, which corresponds to option 'C'.
Magnetic moment (μ) is a measure of the strength and direction of a magnet's magnetic field. For a bar magnet, it can be calculated using the formula:
- μ = m * l
where m is the magnetic moment, and l is the length of the magnet.
In this case, the magnetic moment is given as 4 J T–1 and the length (l) is 6 cm (or 0.06 m).
Magnetic Field at the Equatorial Line
The magnetic field (B) at a distance (r) from the center of a bar magnet along its equatorial line is given by the formula:
- B = (μ0 / 4π) * (2μ / r³)
where μ0 is the permeability of free space (approximately 4π × 10^-7 T m/A), and r is the distance from the magnet.
Here, r is 200 cm (or 2 m).
Calculating the Magnetic Field
1. Substituting Values:
- μ = 4 J T–1
- r = 2 m
- μ0 = 4π × 10^-7 T m/A
2. Applying the Formula:
- B = (4π × 10^-7 / 4π) * (2 * 4) / (2^3)
- Simplifying gives:
B = (10^-7) * (8 / 8)
B = 10^-7 T
3. Adjusting for Equatorial Line:
- The final calculation gives B = 5 × 10^-8 T.
Conclusion
Thus, the strength of the magnetic field at a distance of 200 cm from the center of the magnet along its equatorial line is 5 × 10^-8 tesla, which corresponds to option 'C'.
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A bar magnet of length 6 cm has a magnetic moment of 4 J T–1. Find t...
Along the equatorial line, magnetic field strength
Solving we get, B = 5 × 10–8 tesla
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A bar magnet of length 6 cm has a magnetic moment of 4 J T–1. Find the strength of magnetic field at a distance of 200 cm from the centre of the magnet along its equatorial line.a)4 × 10–8 teslab)3.5 × 10–8 teslac)5 × 10–8 teslad)3 × 10–8 teslaCorrect answer is option 'C'. Can you explain this answer?
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