Two long, parallel conductors, separated by 11.0 cm, carry currents in the same
ID: 1551098 • Letter: T
Question
Two long, parallel conductors, separated by 11.0 cm, carry currents in the same direction. The first wire carries a current I1 = 2.00 A, and the second carries I2 = 8.00 A. (See figure below. Assume the conductors lie in the plane of the page.)
(a) What is the magnetic field created by I1 at the location of I2?
a.)in the +x direction
b.)in the -x direction
c.) in the +y direction
d.) in the -y direction
e.)in the +z direction
f.) in the -z direction
(b) What is the force per unit length exerted by I1 on I2?
a.) in the +x direction
b.)in the -x direction
c.)in the +y direction
d.)in the -y direction
e.) in the +z direction
f.) in the -z direction
(c) What is the magnetic field created by I2 at the location of I1?
a.) in the +x direction
b.) in the -x direction
c.)in the +y direction
d.)in the -y direction
e.)in the +z direction
f.) in the -z direction
(d) What is the force per length exerted by I2 on I1?
a.) in the +x direction
b.)in the -x direction
c.) in the +y direction
d.) in the -y direction
e.) in the +z direction
f.) in the -z direction
magnitude ______________T directiona.)in the +x direction
b.)in the -x direction
c.) in the +y direction
d.) in the -y direction
e.)in the +z direction
f.) in the -z direction
zExplanation / Answer
a)
From Ampere’s law, the B field generated by a long, thin current is
B1 = uoI1 / 2pir
B1 = (4pi x 10^-7 x 2) / (2 x pi x 0.11)
B1 = 3.6363 uT
This B field depends on your distance from I1, but because the wires are parallel, the B field from I1 is constant along I2 We can use the right hand rule to determine that B1 is perpendicular to both I1 and r.
b)
From FB = qv x B we have the force on a current carrying wire in a uniform magnetic field as
FB = Il x B
Combining these two equations, we have the force per unit length of I1 on I2 as
FB12 / l = uoi1i2 / 2pir
= (2 x 10^-7 x 2 x 8) / 0.11
= 29 uN/m
where there is no sin term in the cross product, because B1 is perpendicular to I2. By drawing the situation and doing some right hand rules, you can convince yourself that this force is attractive.
c)
B2 = uoI1 / 2pir
= (2 x 10^-7 x 8) / 0.11
= 14.54 uT
d)
we have another attractive force at the same magnitude,
FB12 / l = 29 uN/m
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.