Question

.5. A square loop of wire (side a) lies on a table a distance s from a very long straight . Suppose a is impase perpendicular to the loop and fills the entire region. (a) Find the flux of B through the loop If someone now pulss the loop directly way from the wire, at speed v, what emf is generated? In what direction (clockwise or counterclockwise) does the current flow? (c) What if the loop is pulled to the right at speed v, instead of away? Figure 2: Square loop and straight wire relevant to #5

Answer 1

a)

consider a small width "dr" of the square loop at distance "r" from the long wire carrying current "I"

dA = small area of the loop at distance "r" from wire = a dr

magnetic field by the long wire at distance "r" is given as

B = ($\mu _{o}$/4$\pi$) (2I/r)

small magnetic flux through small area is given as

d$\phi$ = B dA

d$\phi$ = ($\mu _{o}$/4$\pi$) (2I/r) (a dr)

d$\phi$ = ($\mu _{o}$/4$\pi$) (2Ia) (dr/r)

total magnetic flux through the loop is given as

$\phi$ = $\int_{s}^{s+ a}$ ($\mu _{o}$/4$\pi$) (2Ia) (dr/r)

$\phi$ = ($\mu _{o}$/4$\pi$) (2Ia) ln ((s + a)/a)

b)

induced emf is given as

E = - d$\phi$/dt

E = - (d/dt) ($\mu _{o}$/4$\pi$) (2Ia) ln ((s + a)/a)

E = -($\mu _{o}$/4$\pi$) (2Ia) (ds/dt)/(s+a)

E = -($\mu _{o}$/4$\pi$) (2Ia) (v/(s + a))

c) if the loop is pulled to right , there would be no change in the magnetic flux of the loop. hence induced emf will be 0