Magnetic Field Calculation in a Solenoid

How much current should a solenoid carry to produce a field of 0.353 T at its center?

Length of the solenoid: 28 cm

Diameter of the solenoid: 1.25 cm

Number of turns of the wire: 97

Answer

The solenoid should carry a current of 810.9 A

Calculating the current needed in a solenoid to produce a magnetic field of 0.353 T at its center requires the use of the formula [tex]B=\\mu _0ni[/tex], where B is the magnetic field, [tex]\\mu _0[/tex] is the permeability of free space, n is the number of turns, and i is the current.

Given that the length of the solenoid is 28 cm and the magnetic field is 0.353 T, we can calculate the current by rearranging the formula as follows:

[tex]0.353=\\frac{4\\pi \\times 10^{-7}\\times 97\\times i}{0.28}[/tex]

Solving for the current i, we find that it should be 810.9 A in order to generate a magnetic field of 0.353 T at the center of the solenoid.