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A magnet of length 10 cm and magnetic moment 1 Am2 is placed along the side AB of an equilateral triangle ABC. If the length of side AB is 10 cm, then the magnetic field at point C is
- a)10-9 T
- b)10-7 T
- c)10-5 T
- d)10-4 T
Correct answer is option 'D'. Can you explain this answer?
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A magnet of length 10 cm and magnetic moment 1 Am2is placed along the ...
The magnetic field at point C due to a magnet placed along side AB of an equilateral triangle ABC can be calculated using the formula for the magnetic field due to a magnetic dipole.
Given:
- Length of magnet, l = 10 cm = 0.1 m
- Magnetic moment, M = 1 Am²
- Length of side AB of the equilateral triangle, s = 10 cm = 0.1 m
Formula:
The magnetic field at a point on the perpendicular bisector of a magnetic dipole can be calculated using the formula:
B = (μ₀/4π) * (2M/d³)
where B is the magnetic field, μ₀ is the magnetic constant (4π x 10⁻⁷ Tm/A), M is the magnetic moment, and d is the distance from the dipole.
We need to find the magnetic field at point C, which is the midpoint of side AB.
Step 1: Calculate the distance from the dipole
The distance from the dipole to point C can be found using the Pythagorean theorem since the equilateral triangle ABC has sides of length s.
Using the Pythagorean theorem:
d = √((s/2)² + l²)
= √((0.1/2)² + (0.1)²)
= √(0.025 + 0.01)
= √0.035
≈ 0.187 m
Step 2: Calculate the magnetic field
Using the formula for the magnetic field:
B = (μ₀/4π) * (2M/d³)
= (4π x 10⁻⁷ Tm/A) / (4π) * (2 x 1 Am²) / (0.187)³
= (10⁻⁷) * (2) / (0.187)³
= 2 x 10⁻⁷ / (0.187)³
≈ 2 x 10⁻⁷ / 0.00656
≈ 3.05 x 10⁻⁵ T
≈ 10⁻⁴ T
Therefore, the magnetic field at point C is approximately 10⁻⁴ T, which corresponds to option D.
Given:
- Length of magnet, l = 10 cm = 0.1 m
- Magnetic moment, M = 1 Am²
- Length of side AB of the equilateral triangle, s = 10 cm = 0.1 m
Formula:
The magnetic field at a point on the perpendicular bisector of a magnetic dipole can be calculated using the formula:
B = (μ₀/4π) * (2M/d³)
where B is the magnetic field, μ₀ is the magnetic constant (4π x 10⁻⁷ Tm/A), M is the magnetic moment, and d is the distance from the dipole.
We need to find the magnetic field at point C, which is the midpoint of side AB.
Step 1: Calculate the distance from the dipole
The distance from the dipole to point C can be found using the Pythagorean theorem since the equilateral triangle ABC has sides of length s.
Using the Pythagorean theorem:
d = √((s/2)² + l²)
= √((0.1/2)² + (0.1)²)
= √(0.025 + 0.01)
= √0.035
≈ 0.187 m
Step 2: Calculate the magnetic field
Using the formula for the magnetic field:
B = (μ₀/4π) * (2M/d³)
= (4π x 10⁻⁷ Tm/A) / (4π) * (2 x 1 Am²) / (0.187)³
= (10⁻⁷) * (2) / (0.187)³
= 2 x 10⁻⁷ / (0.187)³
≈ 2 x 10⁻⁷ / 0.00656
≈ 3.05 x 10⁻⁵ T
≈ 10⁻⁴ T
Therefore, the magnetic field at point C is approximately 10⁻⁴ T, which corresponds to option D.
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A magnet of length 10 cm and magnetic moment 1 Am2is placed along the ...
Let m be the pole strength of each pole of the magnet figure. The magnetic field at C due to the N-pole is given by
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A magnet of length 10 cm and magnetic moment 1 Am2is placed along the side AB of an equilateral triangle ABC. If the length of side AB is 10 cm, then the magnetic field at point C isa)10-9Tb)10-7Tc)10-5Td)10-4TCorrect answer is option 'D'. Can you explain this answer?
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