Question

The x, y, and z components of a magnetic field are Bx = 0.10 T, By = 0.14 T, and Bz = 0.17 T. A 25-cm wire is oriented along the z axis and carries a current of 4.4 A. What is the magnitude of the magnetic force that acts on this wire?

Answer 1

we will calculate magnetic force due to each component separately

Bx = 0.10 T, By = 0.14 T, Bz = 0.17 T

L= 25 cm = 0.25 m

I = 4.4 A

Current is flowing along the z-axis

due to Bx first

the angle between Bx and current is 90 degree

F = I*Bx*L Sin 90

F = (4.4)(0.10)(0.25) Sin90

F = 0.11 N

using Right hand rule we can see that its direction will be along y axis

due to By

the angle between By and current is 90 degree

F = I*Bx*L Sin 90

F = (4.4)(0.14)(0.25) Sin90

F = 0.154 N

using Right-hand rule we can see that its direction will be along -x-axis

due to Bz

the angle between Bx and current is 0 so force F will also be zero

so we have two components of F both are perpendicular to each other

as one is along the y-axis and another is along -x-axis

we can find out magnitude using this

F = sqrt(Fx^2 + Fy^2)

F = sqrt((0.154^2) + (0.11^2))

F = 0.189 N