Question for electromagnetic induction

[shubhxxx]

Homework Statement

a conducting rod of length 1 m is rotated with an angular frequency of 400/s about an axis normal to the rod passing through one of its ends .the other end of the rod is in contact with a circular metallic ring. a constant magnetc field of 0.5T parallel to the axis exists in the region.find the emf induced between the ends of the rod.

Homework Equations

|e|=B*pi*ln

The Attempt at a Solution

 

[anathema]

First, we need to calculate the velocity of the rod as it rotates. Since the angular frequency is given in units of radians per second, we can convert it to linear velocity by multiplying by the radius (in this case, the length of the rod), giving us v=400 m/s.

Next, we can use Faraday's law of induction to calculate the induced emf. This law states that the induced emf is equal to the rate of change of magnetic flux through a surface. In this case, the surface is the circular ring, and the magnetic flux is given by the product of the magnetic field, the area of the ring, and the cosine of the angle between the magnetic field and the normal vector of the ring (which is also the axis of rotation of the rod).

Since the magnetic field and the area are constant, we can simplify this equation to e=-B*A*v*cos(theta). The angle theta is the angle between the magnetic field and the normal vector, which in this case is 90 degrees, making the cosine term equal to 0.

Plugging in the values, we get e=-0.5*π*(1m)*(400 m/s)*0=-200π mV. So the emf induced between the ends of the rod is -200π mV.

It's worth noting that the negative sign indicates that the induced current will flow in the opposite direction of the rotation of the rod.