The diagram above shows segments of two long straight wires, carrying currents I

Question

The diagram above shows segments of two long straight wires, carrying currents I1 = 4.0   and I2 = 3.4 respectively. The distance between the wires is 6.8 cm.

A) What is the magnitude of the force per unit length between these two wires – both magnitude and direction? Answer: ______________.___x 10 N/m

B) How far to the right of wire I1 is the total magnetic field due to both currents equal to zero? Answer: _____________.___ cm

C) Now consider the charge q = 3.1 x 10 C, located a distance of 2.9 cm to the right of wire I2, moving to the right at speed v = 46.6 m/s. What is the magnitude of the total magnetic force on this charge? Answer: ____________.___x 10 N

Explanation / Answer

A) magnitude of force per unit length = u0 * I1 * I2/(2pi * d)

magnitude of force per unit length = 4pi *10^-7 * 4 * 3.4/(2pi * 0.068)

magnitude of force per unit length = 4 *10^-5 N/m

the magnitude of force per unit length is 4 *10^-5 N/m

direction of force is towards each other

b)

let the distance is x

for the magnetic field to be zero

u0 * I1/(2pi * x) = u0 * I2/(2pi * (d -x))

4/x = 3.4/(6.8 - x)

solving for x

x = 3.67 cm

the distance from I1 is 3.67 cm

c)

magnetic field at this point , B = 4pi*10^-7/(2pi) * (4/(0.029 + 0.068) + 3.4/.029)

B = 3.17 *10^-5 T

magnitude of total magnetic force = B * v * q

magnitude of total magnetic force = 3.17 *10^-5 * 3.1 *10 * 46.6

magnitude of total magnetic force = 0.046 N

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