Question

Consider a system consisting of two concentric solenoids, asillustrated in the figure. The current in the outer solenoid isI₁ = 1.25 A, and the current in the innersolenoid is I₂ = 2.17 A. The number of turnsper centimeter is 100 for the outersolenoid and 43 for the innersolenoid.

A) Find the magnitude and direction of the magnetic field betweenthe solenoids.

B)Find the magnitude and direction of magnetic field inside theinner solenoid.

Answer 1

Let us take the axis of solenoids as x - axis with positivedirection as right.

The current in the outer solenoid is I₁ =1.25 A,

current in the inner solenoid is I₂= 2.17 A

A )We know that for ideal solenoids magnetic field between thetwo solenoids is magnetic field due to outer solenoid.

B _bet= B_out=-μ₀n₁I₁

n1 = number of turns per unit length of outer solenoid =100 turns/cm = 10000 turns/m

μ₀ = 4π*10^-7H/m

Then B _bet=-( 4π*10^-7H/m)*(10000 turns/m)*1.25A) = -15.7*10^-3T

B) Now net magnetic field inside the inner solenoid is

   B _in = B _out +B_inner

B_inner = magnetic field dueto inner solenoid =μ₀n₂I₂

n2 = 43 turns/cm = 4300turns/m

Then  B _in =-μ₀n₁I₁ +  μ₀n₂I₂

                   = -15.7*10^-3T+-( 4π*10^-7H/m)*(4300turns/m)*2.17 A)

                    = -15.7*10^-3T+11.71*10^-3T

                   =-3.99*10^-3T