Given:
- A very short bar magnet of magnetic moment M
- Magnetic field at a point at a distance d from the centre on axial line of the magnet is B
- Magnetic field at a distance 2d from centre on equatorial line of magnet of magnetic moment 8 M is to be found.

To find: The magnetic field at a distance 2d from centre on equatorial line of magnet of magnetic moment 8 M.

Solution:
Let's consider the magnetic field at a point P on the equatorial line of the magnet at a distance 2d from the centre.

Magnetic field at point P due to the short bar magnet of magnetic moment M:
- Consider a small element dl of the bar magnet at a distance x from the centre on the equatorial line.
- Magnetic field at point P due to this small element dl is given by the formula:
dB = μ₀/4π * (2M/x³) * dl sinθ
where μ₀ is the permeability of free space, θ is the angle between the line joining dl and P and the axial line of the magnet.

- As we move along the equatorial line, the angle θ changes from 0 to 90 degrees.
- At the centre of the magnet (x = 0), the magnetic field due to all the small elements on the magnet cancel out.
- At a distance 2d from the centre (x = 2d), the angle θ is 90 degrees and sinθ = 1.
- Hence, the magnetic field at point P due to the short bar magnet of magnetic moment M is given by:
B₁ = μ₀/4π * (2M/(2d)³) * ∫dl = μ₀/4π * M/d³ * ∫dl

- The integral ∫dl represents the total magnetic moment of the bar magnet which is equal to M.

- Therefore, B₁ = μ₀/4π * M/d³ * M = μ₀/4π * (M/d³)^2

Magnetic field at point P due to the short bar magnet of magnetic moment 8M:
- Since the magnetic moment is 8 times larger, the magnetic field at point P due to this magnet will be 8 times larger than B₁.
- Hence, the magnetic field at a distance 2d from centre on equatorial line of magnet of magnetic moment 8 M is:
B₂ = 8B₁ = 8 * μ₀/4π * (M/d³)^2
B₂/B = 8 * μ₀/4π * (M/d³)^2 / μ₀/4π * (M/d²) = (M/d)² / (M/d³)² = 1/4

Therefore, the magnetic field at a distance 2d from centre on equatorial line of magnet of magnetic moment 8 M is B/4 or B/2 in absolute value (since the direction of the magnetic field is opposite to that of B). Hence, the correct option is (c) B/2.