Question

A car is traveling at 90kph in a region where the horizontal component of the earth's magnetic field has the magnitude 3×10⁻⁵ T. Find the emf induced in the car's vertical radio antenna which is 1.2 m long.

Answer 1

The emf induced in the car's vertical radio antenna is 9x10^-4 V.

Step-by-step explanation:

The induced emf in the car's radio antenna is calculated using Faraday's Law of electromagnetic induction, with the formula ε = Blv sin(θ). Given Earth's magnetic field, the antenna's length, and the car's velocity, one can find the induced emf by converting the velocity to m/s and multiplying it with the antenna's length and the magnetic field's strength. To find the emf induced in the car's vertical radio antenna, we can use the equation:

emf = v * B * l

where v is the velocity of the car, B is the magnitude of the horizontal component of the Earth's magnetic field, and l is the length of the antenna.

Given: v = 90 kph = 25 m/s, B = 3x10-5 T, l = 1.2 m

1. Convert the velocity from kph to m/s: 90 kph * (1000 m/3600 s) = 25 m/s
2. Plug the values into the equation: emf = 25 m/s * 3x10-5 T * 1.2 m = 9x10-4 V

Therefore, the emf induced in the car's vertical radio antenna is 9x10-4 V.