Three long wires parallel to the x axis carry currents as shown.If I = 20 A,what is the magnitude of the magnetic field at the origin?
A)37 $\mu$T
B)28 $\mu$T
C)19 $\mu$T
D)47 $\mu$T
E)58 $\mu$T

Question

Three long wires parallel to the x axis carry currents as shown.If I = 20 A,what is the magnitude of the magnetic field at the origin? 
A)37 $\mu$T 
B)28 $\mu$T 
C)19 $\mu$T 
D)47 $\mu$T 
E)58 $\mu$T

Quizplus · Accepted Answer

The magnetic field at the origin due to each wire can be calculated using the formula:
B = μ0I/2πr, where μ0 is the permeability of free space, I is the current, and r is the distance from the wire.
For the wire carrying 20 A, the distance to the origin along the x-axis is 2 cm, so the magnetic field at the origin due to this wire is:
B1= μ0I/2πr = (4π×10-7 T·m/A)(20 A)/(2π×0.02 m) = 10-4 T.
Since the wires are parallel and in the same direction, the magnetic field at the origin due to all three wires will be in the same direction and can be added together as scalar quantities. Thus, the total magnetic field at the origin is:
Btotal = B1 + B2 + B3 = 3B1 = 3×10-4 T = 19 μT (microtesla).
Therefore, the best choice is (C).

Three Long Wires Parallel to the X Axis Carry Currents μ\muμ

Three Long Wires Parallel to the X Axis Carry Currents $\mu$