Answer to Question #297991 in Electricity and Magnetism for EDEN

Question

A current in a conductor produces a magnetic field that can be calculated using the Biot – Savart law. Because cur- rent is defined as the rate of flow of charge, what can you conclude about the magnetic field produced by stationary charges? What about that produced by moving charges?

Describe the change in the magnetic field in the interior of a solenoid carrying a steady current I (a) if the length of the solenoid is doubled but the number of turns remains the same and (b) if the number of turns is doubled but the length remains the same.

Answer 1

Bio swart law

$B=\frac{\mu_0}{4\pi}\times\frac{I dlsin\theta}{r^2}$

The magnetic field produced by a stationary charge is zero. A moving charge is a current so it will produce a magnetic field.

(1)

Solenoid

Magnetic field

$B=\frac{\mu_0 Ni}{L}$

$L'=2L$

$B'=\frac{\mu_0 Ni}{L'}$

$\frac{B'}{B}=\frac{L}{L'}$

Put value

$B'=\frac{B}{2}$

(2)N'=2N

$B=\frac{\mu_0 Ni}{L}$

$B'=\frac{\mu_0 N'i}{L}$

$\frac{B'}{B}=\frac{N'}{N}$

Put value

$B'=2B$