Near San Francisco, where the vertically downward component of the earth's magnetic field is 6.8...

Question:

Near San Francisco, where the vertically downward component of the earth's magnetic field is 6.8 x 10{eq}^{-5} {/eq} 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

Faraday's law of Electromagnetic Induction :

The result of Faraday's experiments on electromagnetic induction have been summed up in the form of two laws which are known as the laws of Faraday's electromagnetic induction :

{eq}First\ Law : {/eq} When the magnetic flux through a circuit is changing, an induced emf is set up in the circuit whose magnitude is equal to the negative rate of change of magnetic flux.

{eq}Second\ Law : {/eq} The direction of the induced emf, or the current, in any circuit is such as to oppose the cause that produces it.

Answer and Explanation:

Given:

  • The magnetic field, {eq}B = 6.8 \times 10^{-5}\ T {/eq}
  • Width of car, {eq}L = 2.1\ m {/eq}
  • Speed of car, {eq}v = 17\ m/s {/eq}

emf

{eq}\begin{align} e &= BLv\\ &= 6.8 \times 10^{-5}\ T \times 2.1\ m \times 17\ m/s\\ &= 0.0024276\ V \end{align} {/eq}

The direction of induced emf is given by Fleming's right hand rule and we find that charge will accumulate in driver sided.


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