Near San Francisco, where the vertically downward component of the earth's magnetic field is 6.8 x 10-5 T, a car is traveling forward at 17 m/s. The width of the car is 2.1 m. Find the emf induced between the two sides of the car. If positive charge accumulates on the driver's side, the enter the emf as a positive number. If negative charge accumulates on the driver's side, the enter the emf as a negative number.
To find the emf induced between the two sides of the car, we can use Faraday's law of electromagnetic induction, which states that the emf induced is equal to the rate of change of magnetic flux through a surface.
The magnetic flux (Φ) through a surface is given by the product of the magnetic field (B) and the area (A) perpendicular to the magnetic field:
Φ = B * A
In this case, the magnetic field (B) is the vertically downward component of the Earth's magnetic field, given as 6.8 x 10^-5 T.
The area (A) is the width of the car, given as 2.1 m.
Therefore, Φ = (6.8 x 10^-5 T) * (2.1 m).
Next, we need to consider the rate of change of magnetic flux. Since the car is moving forward at 17 m/s, the area (A) perpendicular to the magnetic field is changing with time.
The rate of change of magnetic flux (dΦ/dt) is given by:
dΦ/dt = B * (dA/dt)
Since the car is moving in a straight line, the derivative of the area with respect to time (dA/dt) is equal to the velocity (v) of the car:
dΦ/dt = B * v
Substituting the given values, we have:
dΦ/dt = (6.8 x 10^-5 T) * (17 m/s)
Finally, we can calculate the emf induced (ε) using Faraday's law:
ε = -dΦ/dt
ε = -(6.8 x 10^-5 T) * (17 m/s)
Simplifying the expression gives us the final answer for the emf induced between the two sides of the car.