Question

Suppose a 1-m length of aluminum wire 0.001 m in diameter is held in a horizontal east-west position (in vertical equilibrium) by an external magnetic eld directed north of strength 1 G = 10-4 T. The density aluminum = 2:70 103 kg/m3 and the resistivity aluminum = 2:65 10?8 m. Also note the volume of a cylinder is Vcyl = r2h.

(a) Find the resistance RAl of the aluminum wire.

(b) Find the volume VAl of the aluminum wire.

(c) Find the mass mAl of the aluminum wire.

(d) Write a sentence that explains why the force on the wire from the magnetic eld must be vertically upward (up from the surface of the Earth).

(e) Write a sentence that explains in what direction the current in the wire needs to be so that the force on the wire is vertically upward.

(f) Use Newton's second law for the wire in vertical equilibrium to nd the current Iwire that must be owing in the wire.

(g) Use your answer to parts (a) and (f) to nd the potential dierence Vwire that must exist from one end of the wire to the other.

(h) Use your answer to part (g) to nd the magnitude of the electric eld that exists within the wire from one end to the other.

(i) (2 points) Write a sentence that explains whether the electric eld is directed from-east-to-west or from-west-to-east in the wire

Answer 1

see the diagram :

N = North is into the plane of figure

S = South is out of plane of figure

E = East towards right

W = West towards left

given :

L = 1 m

d = 0.001 m

r = d/2 = 0.0005 m

B = magnetic field = 10^-4 T

density =

resistivity =

a) Resistance of a wire is given by [where A = cross-section area]

therefore, resistance of wire is [answer]

b) A wire is generally a cyclinder in shape.

Therefore, volume of wire = [answer]

c) Mass of a body = density * volume

Therefore, mass of wire = density of wire * density of wire

=> m = [anser

d) given that the wire is in vertical quilibrium.

For vertical equilibrium, the net force along vertical is zero.

in our problem, there are only forces which are in vertical and they must cancel each other .

As force due to gravity is vertically downward, therefore Magnetic force must be in upward direction to balance weight of object.

e) Magnetic force on a current carrying wire is given by

we know the directions of Fwire along vertically upward and B along into the plane of figure.

Applying crossproduct on th equation

we get the direction of vector L which is directed from West to East.