at what velocity must a conductor 75mm long cut a magnetic field of flux density 0.6T if an emf of 9V is to be induced in it? Assuming the conductor, the field and the direction of motion are mutually perpendicular.
Isn't there an equation for this?
E = BLv,
v = E/BL = 9 /0.6•0.075 = 200 m/s
physics
To find the velocity at which the conductor must cut the magnetic field, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced electromotive force (emf) is equal to the rate of change of magnetic flux through the conductor.
The magnetic flux (Φ) through a conductor is given by the product of the magnetic field (B), the perpendicular area (A) through which the field passes, and the cosine of the angle (θ) between the magnetic field and the area vector:
Φ = B * A * cos(θ)
In this case, we are given the values for the magnetic field (B = 0.6 T), the length of the conductor (l = 75 mm = 0.075 m), and the emf (E = 9 V). We need to find the velocity (v) at which the conductor must cut the magnetic field.
Since the conductor, the field, and the direction of motion are mutually perpendicular, the angle (θ) between the magnetic field and the area vector is 90 degrees. Therefore, the cosine of 90 degrees is 0, and the area of the conductor does not affect the calculation.
Now, rearranging the formula for magnetic flux, we get:
Φ = B * A * cos(θ) --> Φ = B * A * 0 --> Φ = 0
Since the magnetic flux is zero, there is no change in flux, and therefore no induced emf, unless the conductor moves. So, for an emf of 9V to be induced, the conductor must move with a velocity that ensures a change in magnetic flux.
Using Faraday's law, we have:
E = (-dΦ / dt)
Since the magnetic flux (Φ) is zero initially, and the final magnetic flux remains zero, we have:
E = 0 - 0 / t --> E = 0 / t --> E = 0
We see that E = 0, which means that no emf is induced unless there is a change in magnetic flux.
Hence, the given scenario is not physically possible as described. In order to induce an emf of 9V in the conductor, there must be a change in the magnetic flux through it, which requires the conductor to move relative to the magnetic field.