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

Question

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

Answer 1

Are we to assume the car is traveling in the horizontal direction? In San Francisco?

Given that assumption (LOL), then the
voltage=velocity*B*length=6.8E-5*17*2.1
= = 0.0024276volt

Now the sign. Use the left hand rule for generators, see http://electriciantraining.tpub.com/14177/css/14177_38.htm I am tired now, but my middle finger points to the passenger side. Check that.

Answer 2

To find the electromotive force (emf) induced between the two sides of the car, we can use Faraday's Law of electromagnetic induction. This law states that the emf induced in a conductor is equal to the rate of change of magnetic flux experienced by the conductor.

First, let's calculate the magnetic flux. In this case, the magnetic field is given as 6.8 x 10^(-5) T, and the width of the car is 2.1 m. So, the magnetic flux (Φ) through the car is:

Φ = B * A

Where B is the magnetic field, and A is the area perpendicular to the magnetic field. Since the magnetic field is perpendicular to the width of the car, the area in this case is the width of the car multiplied by the length of the car (assuming it is moving perpendicular to the magnetic field). However, the length of the car is not given in the information provided, so we cannot calculate the exact value of Φ.

Given that the car is traveling forward at 17 m/s, we can assume that it takes some amount of time for the car to pass through the magnetic field. Let's say this time is Δt.

Now, the rate of change of magnetic flux (dΦ/dt) is given by:

dΦ/dt = (Φ_final - Φ_initial) / Δt

We assume the initial flux (Φ_initial) is zero, as the car has not entered the magnetic field yet. The final flux (Φ_final) is Φ, the flux through the entire car.

So, the rate of change of magnetic flux (dΦ/dt) is:

dΦ/dt = Φ / Δt

Now, according to Faraday's Law, the induced emf (ε) is equal to the negative of the rate of change of magnetic flux:

ε = -dΦ/dt = -Φ / Δt

However, since we are looking for a positive emf when positive charge accumulates on the driver's side, we can assign a negative sign to the magnitude and represent it as a positive number:

emf = |ε|

Now, if you were provided the length of the car or the time taken to pass through the magnetic field, you could calculate the emf using this formula. Without that information, it is not possible to determine the numerical value of the emf in this particular case.