Question

(a) A single long wire has a current of 1.5A flowing through it. Calculate the magnitude of the magnetic field a distance 1m away from the wire.

(b) Make a sketch of the wire and clearly indicate the direction of the current and magnetic field described in part (a).

Four parallel long wires are placed along the edges of a cube of side L=23 cm. Each wire has a current of 1.5A running through it. All currents are in the same direction.

(c) Find the magnitude of the magnetic field at the center of the cube.

(d) Find the magnitude of the magnetic field at the position of one of the conductors due to the other three.

Answer 1

a) given I = 1.5 m
r = 1 m
B = ?

B = mue*I/(2*pi*r)

= 4*pi*10^-7*1.5/(2*pi*1)

= 3.0*10^-7 T

b)

c) at the center, Bnet = 0

d) at the location of the fourth wire

|B1| = |B2| = mue*I/(2*pi*L)

= 4*pi*10^-7*1.5/(2*pi*0.23)

= 1.30*10^-6 T

but B1 and B2 are perpendicualr to each other.

so,

B12 = sqrt(2)*B1

= sqrt(2)*1.3*10^-6

= 1.84*10^-6 T

B3 = mue*I/(2*pi*sqrt(2)*L)

= 4*pi*10^-7*1.5/(2*pi*sqrt(2)*0.23)

= 9.22*10^-7 T

B12 and B3 are parallel.

so, Bnet = B12 + B3

= 1.84*10^-6 + 9.22*10^-7

= 2.76*10^-6 T