Question

(8c29p36) Suppose in the figure that the four identical currents i = 9 A, into or out of the page as shown, form a square of side 102 cm. What is the force per unit length (magnitude and direction) on the wire in the bottom left hand corner? (N/m) Take the positive y direction as up and the positive x direction as to the right. What is the magnitude of the force per unit length? .000016N/m Check the units for MKS. Submit Answer Incorrect. Tries 5/10 Previous Tries What is the x component of the force per unit length? -7.94E-6N/m Submit Answer Incorrect. Tries 5/10 Previous Tries What is the y component of the force per unit length? Submit Answer Tries 0/10

Answer 1

We know that force per unit length is given by:

F/L = u0 i1i2/2pir

So x component of force = -u0i^2/2pia - u0i^2/[2pia*sqrt2]*cos 45 degree

= -2e-7*9^2/1.02 -2e-7*9^2/(1.02*sqrt2) *1/sqrt2

= -0.00001588 - 0.00000794

= -0.00002382 N/m

So y component of force = -u0i^2/2pia - u0i^2/[2pia*sqrt2]*cos 45 degree

= 2e-7*9^2/1.02 -2e-7*9^2/(1.02*sqrt2) *1/sqrt2

= 0.00001588 - 0.00000794

= 0.00000794 N/m

Net force magnitude = sqrt(0.00002382^2+0.00000794^2) = 0.0000251 N/m answer

x component = -0.00002382 N/m answer

y component = 0.00000794 N/m answer