Magnetic Field involving solenoids

McAfee

1. The problem statement, all variables and given/known data

Two long ideal solenoids (with radii 20 mm and 30 mm respectively) carry the same number of turnes of wire per unit length. The smaller solenoid is mounted inside the larger, along a common axis. It is observed that the magnetic field within the inner solenoid is zero. The current in the inner solenoid must be:

A. two-thirds the current in the outer solenoid
B. one-third the current in the outer solenoid
C. twice the current in the outer solenoid
D. half the current in the outer solenoid
E. the same as the current in the outer solenoid

This one is hard. If you could please provide an explanation with the answer so I could better understand this.
THanks in advance.

2. Relevant equations

n/a

3. The attempt at a solution

Right now I'm ruling out answer A.

tiny-tim

Hi McAfee!
Call the currents I and J.

Hint: what is the formula for the magnetic field inside a current-carrying solenoid?

And can we just add the fields?

McAfee

The formula is B = μ_o*i*n

n is the number of turns
and yes

tiny-tim

yup!

so what's the total equation, and is it A B C D or E ?

McAfee

20mm = .02
30mm = .03

assuming that I can ignore n because it will be the same for both.
Would it be E because the radii doesn't play a role in the equation?

tiny-tim

sorry, i missed your post …
yes the radii don't matter,

so if (case E) the currents are equal (and opposite), then the magnetic field inside the inner solenoid will be zero