Find the magnetic field (positive magnitude only, no direction) at point P.

Question

I1=(2.50 A) to P to I2=(3.50 A). I1 to p has a distance of 0.0700 m. P to I2 has a distance of 0.160 m.

Answer 1

Solution:

The formula for the magnetic Field B in Tesla for a point a distance R away from the current is

B = μ₀ I / 2π R

For two positive currents away from point P and based on the location order described in the problem statement, I1 is located to the left of P and I2 to the right of P. The Magnetic Field B is the sum of the magnetic fields created by each of the charges on point P. However, the currents are parallel to each other as they are both positive currents and in the same direction. So, using the right hand and pointing the finger in the direction of the current I1 located to the left of point P, the fingers curl CCW around the current causing a magnetic field perpendicular to the plane of the current and in this case into the paper at P due to I1. For I2 located to the right of P the curl cause a magnetic field that is also perpendicular to I2, but this time out of the paper at P due to I2, and therefore the magnetic field vectors are opposite to each other and subtractive

so B = μ₀ [ ( I1 /2π R1) - ( I2 / 2π R2)] where μ₀ is the permeability of free space = 4π x 10^-7

B = 4π x 10^-7 / 2π [( I1 / R1) - (I2 / R2)] = 2x10^-7 [ ( 2.5 A/ 0.07m) - (3.5A/ 0.160m)] = 13.83 x 10^-7 T

Also note that Tesla (T ) has a units of A/m and A has a unit of C /s , combining T has a unit of C /s .m

or coulomb per second per meter