Question

How strong is the magnetic field inside a solenoid with 10,000turns per meter that carries 20.0 A?

Short answer

The magnetic field strength inside a solenoid carrying 20.0 A current having 10,000 turns per meter is 0.25 T

Step-by-step solution

Definition of magnetic field

A magnetic field is defined as a position in space near a magnet or an electric current where a physical field is formed by a moving electric charge applying force on another moving electric charge.

Given information and formula to used

The number of turns per meter is N=10000

The current in the loop is, I=20.0A

The magnetic field inside a solenoid can be estimated as,

$B={\mu }_0\mathrm{NI}$…………….(1)

Where ${\mu }_0$is the magnetic permeability of free space.

Step 3: Calculation for Magnetic field inside a solenoid:

Substitute the values in the above expression, we will get

$$\begin{gathered} B=\left(4\mathrm{\pi }\times {10}^{-7}\mathrm{N}/{\mathrm{m}}^2\right)\times 10000\times 20.0\mathrm{A} \\ =0.25\mathrm{T} \end{gathered}$$

Therefore, the magnetic field strength inside a solenoid carrying 20.0A current having 10,000 turns per meter is 0.25T .