Acircular loop of wire is rotated at constant angular speed about an axis whose direction can be varied. in a region where a uniform magnetic field points straight down, what must be the orientation of the loop's axis of rotation if the induced emf is to be zero?

here the coil must be oriented in such a way that its plane is perpendicular to the magnetic field

Explanation:

As we know by Faraday's law of electromagnetic induction

Rate of change in magnetic flux will induce EMF in the coil

so here we will have

here we know that

now if the magnetic flux will change with time then it will induce EMF in the coil

so here induced EMF will be zero in the coil if the flux linked with the coil will remain constant

so here the coil must be oriented in such a way that its plane is perpendicular to the magnetic field

In such a way when coil will rotate then the flux linked with the coil will remains constant and there will be no induced EMF in it

the independent variable, or the one that is intentionally manipulated is the speed.

answer: a) y=-8x+5

a) m= -8

b) m= -2

c) m= 7

d) m= 6