An infinitely long wire carries a current of 2 A as shown in the picture. It is
ID: 1287646 • Letter: A
Question
An infinitely long wire carries a current of 2 A as shown in the picture. It is surrounded by a hollow conducting cylinder of inner radius R1 = 2 cm and outer radius R2 3 cm that carries a uniform current of 2 A in the opposite direction.
Using Amperes law:
(a) Find the magnitude of the magnetic field B at a distance r = 1 cm from the axis of the cylinder.
(b) Find the magnitude of the magnetic field B at a distance r = 2.5 cm from the axis of the cylinder.
(c) Find the magnitude of the magnetic field B at a distance r = 4 cm from the axis of the cylinder.
An infinitely long wire carries a current of 2 A as shown in the picture. It is surrounded by a hollow conducting cylinder of inner radius R1 = 2 cm and outer radius R2 3 cm that carries a uniform current of 2 A in the opposite direction. Using Ampere s law: (a) Find the magnitude of the magnetic field B at a distance r = 1 cm from the axis of the cylinder. (b) Find the magnitude of the magnetic field B at a distance r = 2.5 cm from the axis of the cylinder. (c) Find the magnitude of the magnetic field B at a distance r = 4 cm from the axis of the cylinder.Explanation / Answer
let I1 = 2 A
I2 = 2A
a) at r = 1 cm
I_enclosed = I1
= 2A
According to Ampere's law,
integral B.dl = mue*I_enclosed
B*2*pi*r = mue*I1
B = mue*I1/(2*pi*r)
= 4*pi*10^-7*2/(2*pi*0.01)
= 4*10^-5 T <<<<<<----------Answer
b) at r = 2.5 cm
I_enclosed = I1 - I2*pi*(R2^2 - r^2)/(pi*(R2^2-R1^2)
= 2 - 2*(0.03^2 - 0.025^2/(0.03^2-0.02^2)
= 0.9 A
integral B.dl = mue*I_enclosed
B*2*pi*r = mue*I_elcosed
B = mue*I_enclosed/(2*pi*r)
= 4*pi*10^-7*0.9/(2*pi*0.01)
= 1.8*10^-5 T <<<<<<----------Answer
c) at r = 4 cm
I_enclosed = I1 - I2
= 0
so, B = 0 <<<<<<----------Answer