Question

A very long wire and a square loop of wire lie in the plane of the page as shown. Each side of the square is 15 cm in length, the resistance of the loop is 0.6 Ω, and the near side of the loop is 3 cm from the long wire. The current in the long wire is to the right and is increasing. At the moment, the current in the long wire is 6.5 A. The magnetic flux through the loop is increasing at the rate of 2.8x10 Wb/s. What is the direction of the magnetic field that the long wire creates within the loop? What is the magnitude of the emf induced in the loop? what is the magnitude of the current induced in the loop? ーーーーーーーーーーーーーーーーーーー What is the direction of the current induced in the loop? clockwisecounterclockwise What is the magnitude of the magnetic field that the long wire creates at the near side of the loop? What is the magnitude of the magnetic force on the side of the loop nearest the long wire? What is the direction of the magnetic force on the side of the loop nearest the long wire? xtytZ +X -x

Answer 1

a) the direction of magnetic field inside the loop is along +z

b) induced emf is given by

$\varepsilon =\frac{d\phi }{dt}$

E = 2.8 x 10^-9 v

c) induced current i =E/R

i = (2.8 x 10^-9 v/0.6 ohms) = 4.67 x 10^-9 A

d) direction of induced current would be clock wise

e) magnetic field due to an infinite wire is given by

$B =\frac{\mu _{0}i}{2\pi d}$

here i =6.5 A

d = 3cm = 0.03 m

plugging in we get

B = 4.33 x 10^-5T

f) force experianced is given by

F =ilB

here

i = 4.67 x 10^-9 A

l =15 cm = 0.15m

B = 4.33 x 10^-5T

plugging in we get

F = 3.04 x 10^-14N

g) the direction of currents in the two wires are opposite , hence they would repel

so direction of force is along +y