Find Induced Voltage in Rotating Conductor in Radial Field

[erece]

Homework Statement

A conductor 1 cm in length is parallel to z axis and rotates in a radius of 25 cm at 1200 rev/min , find induced voltage if radial field is given by B = 0.5 a$_{r}$

Homework Equations

The Attempt at a Solution

i am confused. If there is no closed path then how the voltage can be induced

 

[rude man]

Voltage (actually emf) is induced in any material of any kind - even a vacuum! - over a length dL:

dV = (B x dL) * v
where B is magnetic field and v is the velocity of the element of length dL. Vectors in bold.

The direction of dL is in the direction of conventional current under the assumption of a closed circuit. But there need not be a closed circuit.

 

[tiny-tim]

hi erece!

If there is no closed path then how the voltage can be induced

the magnetic field causes a force, so that the electrons to "want" to move along the wire

whether they can is irrelevant … there is a gravitational potential difference between the table and the floor even if the things on the table cannot fall to the floor!

voltage = potential energy difference per charge = work done per charge (V = W/q)

work done = force "dot" displacement

for example, if a rod of length L moves at speed v perpendicularly to a uniform magnetic field B, then the force on a charge q inside the rod is qvB along the rod,

so the work done moving it a distance L along the rod is ∫ qvB dx = qvBL,

and the work done per charge is vBL,

ie V = vBL​

ok, that's for linear motion, where v is constant (along the rod) …

in your case, v changes along the rod, so the work done integral (∫ qvB dx) will be more complicated