Question

2) Consider the arrangement of currents shown A. Obtain a symbolic expression for the total force (magnitude AND direction) exerted on li by l2in terms of given quantities. Using the symmetry of the arrangement might make the expression easier to obtain, but you should justify your reasoning with a BRIEF explanation. (10 pts) Calculate the numerical magnitude of the force you found in A. (1 pt) ,15.0 A B. 7.50 cm a 10.0 cm 30.0A L-30.0 cm

Answer 1

Given data; I1=15.0 A, I2=30.0 A, r=7.50 cm, l=30.0 cm

The force on vertical sections of the wire will be equal in magnitude but opposite in direction as the current in the left vertical wire flows down but in right vertical wire the current flows up.

A. Force between two parallel current carrying conductor is in general

F = u0*I1*I2*l/2*pi*r

Force on side at 7.50 cm for conductor is

F = u0*I1*I2*l/2*pi*b (this force is repulsive)

Force on side at 17.50 cm for conductor is

F = u0*I1*I2*l/2*pi*(a+b) (this force is attractive)

Net force = u0*I1*I2*l/2*pi*b - u0*I1*I2*l/2*pi*(a+b) = u0*I1*I2*l*a/2*pi*b(a+b)

B. F1 = (4*pi*10^-7)*15*30*(30*10^-2)/2*pi*(7.50*10^-2)
  
= 3.600*10^-4 N

F2 = (4*pi*10^-7)*15*30*(30*10^-2)/2*pi*(17.50*10^-2)

= 1.542*10^-4 N

The net force is

Fnet = F1 - F2

= 3.600*10^-4 N - 1.542*10^-4 N

= 2.058*10^-4 N