Question

what are the factors on which the strength of a magnetic field produced by a current carrying solenoid depends

Answer 1

amount of current flowing 
no of turns of solenoid
material that is placed inside the solenoid should be magnetic like iron rod

Answer 2

Let us consider a solenoid of length' l' . Let n number of turns are present per unit length.

Now, current is allowed to flow through the solenoid. Let the current flowing through each turn is i

The magnetic field produced on a solenoid due to the current flowing through it is calculated as -

                           $B\ =\frac{\mu_{0}ni} {l}$

Hence, from above we see that-

[1] The magnetic field is directly proportional to number of turns

[2] The magnetic field is directly proportional to the current flowing through each turn

[3] The magnetic field is inversely proportional to the length of the solenoid.

[4] The magnetic field is also dependent on the nature material which is present inside the solenoid as core. For instance we may take soft iron for which the  field is more.