If the length and radius were doubled keeping the number of turns and current the same, the magnetic field would be B0/2.
Explanation:
A solenoid is a device that has wires wound in the shape of a cylinder. It is used to generate strong magnetic field by passing current through it. The magnetic field inside a solenoid is determined by the current passing through the solenoid as well as the number of turns per unit length of the solenoid.
The diameter or radius of the solenoid has no effect on the magnetic field inside a solenoid.
B=μ0nI
where μ0 represents the permeability of free space, n represents the number of turns per unit length and I represents the current passing through the solenoid.
n is given by the expression
n=N/L where N is the total number of turns of the solenoid and L is its length
B0=μ0NI/L
in this problem
[tex]Length=2 L_{0}[/tex]
new magnetic field Bnew=μ0NI/2L0=[tex]B_{0} /2[/tex]
Hence the magnetic field will become half of its initial value.
