Consider a wire carrying a current due east in a location where the Earths field
ID: 3278252 • Letter: C
Question
Consider a wire carrying a current due east in a location where the Earths field is due north. (a) What is the direction of the force on the wire if both are parallel to the ground? (b) Calculate the force per unit length on the wire, in newtons per meter, if the wire carries 22.5 A and the field strength is 3.2 times 10^-5 T. (c) What would the diameter be, in meters, of copper wire (with density rho = 8.80 times 10^3 kg/m^3) that would have its weight supported by this force in meters? (d) Calculate the resistance per unit length, in ohms per meter, that this copper wire will have. Copper has a resistivity of rho_R = 1.72 times 10^-8 Ohm middot m. (e) Calculate the potential difference per unit length, in volts per meter, of this wire.Explanation / Answer
a] force F = i L x B
L points east ( x direction), B points north (y direction) so L xB will be upward (z direction)
Force points upward
b] force per unit length = F/L = i B = 22.5*3.2e-5 = 0.00072 N/m
c] let diameter be d
weight = F
0.25 pi d^2 *L* rho*g = 0.00072 L
d = sqrt(0.00072/(0.25*pi*8800*9.8)
= 0.000103 m
d] resistance per unit length = R/L = rhoR/A = 1.72e-8/(0.25*pi*0.000103^2)
= 2.064 ohm/m
e] Potential difference per unit length = iR/L = 2.064*22.5
= 46.4 V/m