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The force between two short bar magnets with magnetic moments M₁ and M₂ whose centres are r meter apart is 8 N, when their axes are in same line. If the separation is increased to 2 r, the force between them is reduced to
  • a)
    4 N
  • b)
    2 N
  • c)
    1 N
  • d)
    0.5 N
Correct answer is option 'D'. Can you explain this answer?
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Given:
M₁ = magnetic moment of first magnet
M₂ = magnetic moment of second magnet
r = separation between the two magnets
F₁ = force between the two magnets when r is separation
F₂ = force between the two magnets when 2r is separation

To find: F₂

Formula:
The magnetic force between two magnets is given by:
F = (μ₀M₁M₂)/(4πr²)

where,
μ₀ = permeability of free space (constant)

Analysis:
When the axes of the two magnets are in the same line, the force between them is maximum.

When the separation between the magnets is doubled, the force between them will decrease.

Solution:
We can use the formula for magnetic force to find the force between the two magnets.

When the separation between the magnets is r:
F₁ = (μ₀M₁M₂)/(4πr²)

When the separation between the magnets is 2r:
F₂ = (μ₀M₁M₂)/(4π(2r)²) = (μ₀M₁M₂)/(16πr²)

We are given that F₁ = 8 N. We can use this to find the value of μ₀M₁M₂.

8 = (μ₀M₁M₂)/(4πr²)
μ₀M₁M₂ = (8)(4πr²)

Substituting this into the equation for F₂:
F₂ = (μ₀M₁M₂)/(16πr²) = [(8)(4πr²)]/(16πr²) = 0.5 N

Therefore, the force between the two magnets when the separation is 2r is 0.5 N.
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The force between two short bar magnets with magnetic moments M₁ and M₂ whose centres are r meter apart is 8 N, when their axes are in same line. If the separation is increased to 2 r, the force between them is reduced toa)4 Nb)2 Nc)1 Nd)0.5 NCorrect answer is option 'D'. Can you explain this answer?
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