Question

Consider two, long parallel wires (labeled a and b) carrying electric currents ia and in respectively in the same directions. The wires are separated by distance d, as shown in the figure below. Interactive Figure 29.4.1: Two long, straight, parallel wires carry currents in the same direction. Figure 29.4.2 shows an end-on view with the two currents directed out of the screen (in the +z direction). Assume the following values for the two currents and the distance d: ia = 1.00 A, ib = 1.50 A, and d = 2.00 m. Wire b

Answer 1

Magnetic field by the current in wire b at the location of wire "a" is given as

B_b = ($\mu _{o}$/4$\pi$) (2 i_b/d)

B_b = (10^-7) (2 (1.50)/2)

B_b = 1.5 x 10^-7 T

B_b = 0.15 x 10^-6 T

B_b = 0.15 $\mu$ T

In unit vector notation

$\underset{B_{b}}{\rightarrow}$ = 0.15 $\mu$ T $\hat{i}$

$\underset{L}{\rightarrow}$ = length of wire a = 0.5 $\hat{k}$

i_a = current in wire a = 1 A

magnetic force on wire "a" is given as

$\underset{F_{ab}}{\rightarrow}$ = i_a ($\underset{L}{\rightarrow}$ x $\underset{B_{b}}{\rightarrow}$ )

$\underset{F_{ab}}{\rightarrow}$ = (1) ((0.5 $\hat{k}$ ) x (0.15   $\hat{i}$ ))

$\underset{F_{ab}}{\rightarrow}$ = 0.075 $\mu$ N $\hat{j}$