show me step by step The figure shows an Amperian loop with currents coming in a

Question

show me step by step

The figure shows an Amperian loop with currents coming in and out of the screen. If 11 = 4.5 A, 12 = 1 A and the value of the line integral of the magnetic field around the loop is 12.4 Tm then what is the value of the current 13 (in A)? (This problem is inspired by problem 32.21 in Knight's 3rd edition) (Hint: Remember to use the right hand rule to assign the correct sign to each current. A positive sign for a given current means that the current creates a magnetic field in the same direction as the arrows around the loop.)

Explanation / Answer

from the amperes law

the line integral of the magnetic induction around a closed path in a magnetic field is equals to the u0 times total current enclosed by the closed path.

so,

12.4 *10^-6 =uo(i1+i3-i2)

i1+i3-i2=12.4*10^-6/4*3.14*10^-7

i1+i3-i2=9.8726

then i3=9.8726-i1+i2

i3=9.8726-4.5+1

i3=6.3726 Ampers

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