To find the coefficient of coupling between two coils, we can use the formula:

k = M / √(L1 * L2)

Where:
k is the coefficient of coupling
M is the mutual inductance between the coils
L1 and L2 are the self-inductances of the two coils

Given:
L1 = 0.09 H
L2 = 0.01 H
M = 0.015 H

Let's substitute these values into the formula to find the coefficient of coupling (k):

k = 0.015 / √(0.09 * 0.01)
k = 0.015 / √(0.0009)
k = 0.015 / 0.03
k = 0.5

Hence, the coefficient of coupling between the two coils is 0.5.

Explanation:
The coefficient of coupling is a measure of how well the magnetic field produced by one coil links with the other coil. It ranges from 0 to 1, where 0 indicates no coupling and 1 indicates perfect coupling.

In this case, the mutual inductance between the coils is given as 0.015 H. Mutual inductance represents the extent to which the magnetic field produced by one coil is linked with the other coil. A higher mutual inductance value indicates a stronger coupling between the coils.

The self-inductance of the first coil is given as 0.09 H and the self-inductance of the second coil is given as 0.01 H. Self-inductance represents the ability of a coil to generate an electromotive force (EMF) in itself when the current through it changes. It does not depend on the presence of any other coil.

By substituting these values into the formula, we find that the coefficient of coupling is 0.5. This indicates that there is a moderate coupling between the coils, meaning that a significant portion of the magnetic field produced by one coil is linked with the other coil.

Hence, the correct answer is option B: 0.5.