How does the strength of an electromagnet depend on the current and the number of turns in the coil ?

Question

schrodingers_cat · Answer

Recall amperes law. 

$$\int\limits B ds = \mu I$$

Where the integral is a line integral over a closed loop and, B and ds are dotted together.

For a solenoid this reduces to 

$$B = \mu nI$$

From here you can see that the strength of the magnetic filed is directly proportional to the number of loops n and the current I. For most electromagnets an iron core is added to the solenoid to magnify the effective strength of the field. The equation then becomes

$$B = k \mu nI$$ 

where k is called the relative permeability.

If you want to know how derive the magnetic field a simple solenoid just let me know.

Hopes this helps :)