Explanation:

To understand why the self inductance of a coil affects the delay in establishing a steady-state current through it, we need to first understand what self inductance and inductance mean.

Inductance is the property of a circuit element (in this case, a coil) that opposes any change in the current flowing through it. It is denoted by the symbol L and is measured in henries (H). Self inductance, specifically, refers to the inductance of a coil due to its own magnetic field.

When a current flows through a coil, it generates a magnetic field around it. This magnetic field links with the coil itself, inducing an electromotive force (emf) in the coil. According to Faraday's law of electromagnetic induction, this emf opposes the change in current flowing through the coil, which is the essence of inductance.

Now, let's consider the options given and see how they relate to the self inductance of the coil:

a) More will be the weber turns: The number of turns in a coil affects the magnitude of the magnetic field generated by the coil. However, it does not directly affect the self inductance of the coil. So this option is not correct in relation to the question.

b) More will be the emf induced: This option is partially correct. The self inductance of a coil is directly proportional to the magnitude of the emf induced in the coil. So, increasing the self inductance will result in a greater emf induced. However, this option does not explain why there would be a smaller delay in establishing a steady-state current.

c) Lesser the flux produced by it: The flux produced by a coil is directly proportional to the self inductance. So, decreasing the self inductance would actually result in a lesser flux produced by the coil. This option is not correct in relation to the question.

d) Smaller the delay in establishing steady-state current through it: This option is correct. The self inductance of a coil determines the opposition to any change in current. A smaller self inductance means less opposition to the change in current, resulting in a smaller delay in establishing a steady-state current through the coil. In other words, the coil reaches steady-state more quickly when its self inductance is smaller.

Therefore, the correct answer is option 'D'.