Question

A very long thin wire carries a current I1 is next to a square wire loop of width L = 5 .0 cm. Both the wire and the loop lay in the same plane with a gap of s = 1 .0 cm between them. The square loop has a break where two parallel plates with surface area A = 4 .0 cm 2 are separated by a gap of d = 1 µm. The radius of the wire that makes up the loop is 0.4 mm and the material of the wire has conductivity of 1 . 0 ×10 6 A V − 1 m − 1 .

a. Qualitatively describe how the induced emf, current, and charges through the wire loop vary

b. Calculate the ratio of charge on the plates to the potential between the plates.

c. Calculate the resistance of the square loop

d. If the current in the long straight wire is given by I2 [ t] = 1 .2 A s − 1 . Calculate the induced emf around the square loop. Be sure to describe your physical reasoning and any assumptions used. You may find it useful to check your results against lower and upper limits that don’t require integration. [Hint: a potentially useful form of the differential area for a square is d A = L d x ]

Answer 1