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The magnetic induction on the equatorial line of a short magnet at distance d from the centre of the magnet is B. At what distance on the equatorial line of the magnet the magnetic induction would become 4B. 1)d/2 2)d/2^1/2 3)d/2^1/3 4)d/2^1/5?
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The magnetic induction on the equatorial line of a short magnet at dis...
Solution:
Given: Magnetic induction on the equatorial line of a short magnet at distance d from the centre of the magnet is B.
To find: At what distance on the equatorial line of the magnet the magnetic induction would become 4B.
Let the distance at which the magnetic induction becomes 4B be x.
We know that on the equatorial line, the magnetic field due to a short magnet at a distance x from the centre of the magnet is given by:
B = μ0/4π * (m/x^3), where m is the magnetic moment of the magnet.
We can rearrange this equation to find x:
x = (μ0/4π * m/B)^(1/3)
Now, we need to find the ratio of x/d:
(x/d) = [(μ0/4π * m/B)^(1/3)] / d
(x/d) = [(μ0/4π * m/B)^(1/3)] * [1/d]
(x/d) = (μ0/4π * m/B*d^3)^(1/3)
(x/d) = (m/2Bd^3)^(1/3)
(x/d) = [m^(1/3)] / [2^(1/3) * B^(1/3) * d^(1/3)]
(x/d) = d/2^(1/3)
Therefore, the distance at which the magnetic induction becomes 4B on the equatorial line of the magnet is d/2^(1/3).
Answer: Option 3 (d/2^(1/3))
Note: The above solution is just a guide to help you understand the steps to solve the problem. It is important to understand the concept and try to solve the problem on your own.
Given: Magnetic induction on the equatorial line of a short magnet at distance d from the centre of the magnet is B.
To find: At what distance on the equatorial line of the magnet the magnetic induction would become 4B.
Let the distance at which the magnetic induction becomes 4B be x.
We know that on the equatorial line, the magnetic field due to a short magnet at a distance x from the centre of the magnet is given by:
B = μ0/4π * (m/x^3), where m is the magnetic moment of the magnet.
We can rearrange this equation to find x:
x = (μ0/4π * m/B)^(1/3)
Now, we need to find the ratio of x/d:
(x/d) = [(μ0/4π * m/B)^(1/3)] / d
(x/d) = [(μ0/4π * m/B)^(1/3)] * [1/d]
(x/d) = (μ0/4π * m/B*d^3)^(1/3)
(x/d) = (m/2Bd^3)^(1/3)
(x/d) = [m^(1/3)] / [2^(1/3) * B^(1/3) * d^(1/3)]
(x/d) = d/2^(1/3)
Therefore, the distance at which the magnetic induction becomes 4B on the equatorial line of the magnet is d/2^(1/3).
Answer: Option 3 (d/2^(1/3))
Note: The above solution is just a guide to help you understand the steps to solve the problem. It is important to understand the concept and try to solve the problem on your own.
Community Answer
The magnetic induction on the equatorial line of a short magnet at dis...
3)d/2^1/3
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The magnetic induction on the equatorial line of a short magnet at distance d from the centre of the magnet is B. At what distance on the equatorial line of the magnet the magnetic induction would become 4B. 1)d/2 2)d/2^1/2 3)d/2^1/3 4)d/2^1/5?
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