Thr diagram above shows segments of two long wires, carrying currents I1 = and t

Question

Thr diagram above shows segments of two long wires, carrying currents I1 = and t2 = A respectively. The distance between the wires is cm. What is the magnitude of the force per unit length between these two wires both magnitude and direction? Answer N/m How far to the of wire I1 is the total magnetic field due to both currents equal to zero? Answer: cm. Now consider the charge q = c, located a distance of cm to the right of wire I2 moving to the right at speed V = m/s. What is the magnitude of the total magnetic force on this charge? ' Answer: N

Explanation / Answer

Use equation,

a) F/L = u0I1I2/(2*pi*r) = (4*pi*10^-7*9.4*2)/(2*pi*0.05) = 7.52*10^-5 N/m

b) Assume this distance = x

B1-B2 = 0

B1=B2

u0I1/(2*pi*x) = u0I2/(2*pi*(r-x))

I1/x= I2/(r-x)

I1/I2= x/(r-x)

9.4/2 = x/(0.05-x)         => 0.412m = 4.12cm

c)

First let us find B at a distance r = 0.0.27m

Both B's wil have same direction hence they add up

Bnet = B1 +B1 = u0I1/(2*pi*1) + u0I1/(2*pi*r2) = u0/(2*pi)*(I1/r1 + I2/r2) = 4*pi*10^-7/(2*pi) *[9.4/(0.05+0.027) + 2/0.027] = 3.92*10^-5 T

Bnet is directed into the page

F = qvB = (73*67.1*3.92*10^-5) = 0.2 N

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