Two long, straight wires separated by 0.10 m carry currents of 18 A and 6 A in the same direction as shown.
-Determine the magnitude of the magnetic field at the point P.

Question

Two long, straight wires separated by 0.10 m carry currents of 18 A and 6 A in the same direction as shown. 
-Determine the magnitude of the magnetic field at the point P.

Quizplus · Accepted Answer

The magnitude of magnetic field at point P due to wire carrying current I is given by:
$$B=\frac{\mu_0I}{2\pi r}$$
where, $\mu_0=4\pi	imes10^{-7}$ T m/A is the permeability of free space and r is the distance between the wire and the point P.
For the wire carrying current 18 A, the field at point P is:
$$ B_1=\frac{\mu_0I_1}{2\pi r}=\frac{4\pi	imes 10^{-7}	imes 18}{2\pi	imes 0.1}=3.6	imes 10^{-5} T$$
For the wire carrying current 6 A, the field at point P is:
$$ B_2=\frac{\mu_0I_2}{2\pi r}=\frac{4\pi	imes 10^{-7}	imes 6}{2\pi	imes 0.1}=1.2	imes 10^{-5} T$$
Since the currents are in the same direction, the total magnetic field at point P due to both wires is the sum of these fields:
$$ B_{total}=B_1+B_2=4.8	imes 10^{-5}T $$
Therefore, the best choice is B.

Two Long, Straight Wires Separated by 0