Which changes will cause an increase in the magnetic field of a solenoid? check all that apply. using more wire loops.
using fewer wire loops.
using a larger current.
using a smaller current.
increasing the spacing. between loops.
decreasing the spacing between loops.

There are three answers that should be marked as changes that increase the magnetic field of a solenoid:

using more wire loops.

using a larger current

decreasing the spacing between loops

Explanation:

Recall the formula for the magnitude of the magnetic field (B) inside a solenoid:

where N is the number of current loops,

I is the current running through the loops,

and L is the length of the solenoid.

We see then that the field is directly proportional to the number of loops, and to the current, therefore, using more wire loops as well as increasing the current, will render an increase in magnetic field.

To analyse the options associated with spacing between loops, notice that the magnetic field is inversely proportional to the total length of the solenoid, therefore if we decrease the solenoid's length, we will also increase the magnetic field inside it. An easy way to do such is to decrease the spacing between the loops.

Therefore there are three answers that should be marked as changes that increase the magnetic field of a solenoid:

using more wire loops.

using a larger current

decreasing the spacing between loops

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y