When a thin 12.0cm iron rod moves with a constant velocity of 6.50m/s perpendicular to the rod, the induced emf across its ends is measured to be 0.300V.

What is the magnitude of the magnetic field?

To find the magnitude of the magnetic field, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced electromotive force (emf) in a conductor is equal to the rate of change of magnetic flux through the conductor.

The induced emf, E, can be expressed as:

E = -N * dΦ/dt

Where E is the induced emf, N is the number of turns in the coil, dΦ/dt is the rate of change of magnetic flux through the coil.

In this case, the iron rod is moving perpendicular to the rod, which means that the magnetic flux through the rod is changing. The induced emf measured across its ends is 0.300V.

Since the rod is thin, we can assume that the entire length of the rod experiences the same magnetic field. Therefore, the induced emf is the same across the entire rod.

We are given the length of the rod as 12.0cm and the velocity of the rod as 6.50m/s.

To find the magnetic field, we first need to determine the rate of change of magnetic flux, dΦ/dt. The rate of change of magnetic flux can be expressed as:

dΦ/dt = E / N

Next, we need to determine the number of turns, N, in the coil. Since the rod is not wrapped around a coil, we can assume that N equals to 1.

Finally, we can substitute the values into the equation:

dΦ/dt = 0.300V / 1 = 0.300 V/s

Now, we can rearrange the equation to solve for the magnetic field, B:

B = (dΦ/dt) / A

Where B is the magnetic field, dΦ/dt is the rate of change of magnetic flux, and A is the cross-sectional area of the rod.

The cross-sectional area of the rod can be calculated as:

A = width * height

Since the rod is thin, we can assume that the width is negligible compared to the length. Therefore, we can use the diameter of the rod to calculate the cross-sectional area.

We are not given the diameter of the rod in the question, so in order to solve for the magnetic field, we need this additional information.