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A car travels northward at 75 km/h along a straight road in a region where Earth's magnetic field has a vertical component of 0.50 * 10−4 T. The emf induced between the left and right side, separated by 1.7 m, is:

A. 0
B. 1.8 mV
C. 3.6 mV
D. 6.4 mV
E. 13 mV

1 Answer

4 votes

Final answer:

The induced electromotive force (emf) between the left and right side of a car traveling northward at 75 km/h in a vertical magnetic field is approximately 1.8 mV.

Step-by-step explanation:

The student's question pertains to the concept of motional emf in physics. The motional emf is calculated using Faraday's law of electromagnetic induction, specifically the equation ε = BvLsinθ, where ε is the induced electromotive force (emf), B is the magnetic field strength, v is the velocity of the conductor, L is the length of the conductor, and θ is the angle between the velocity vector and the magnetic field vector.

In this scenario, the car is traveling northward with a velocity (v) of 75 km/h, which is equivalent to 20.83 m/s (since 75 km/h is 75,000 meters divided by 3600 seconds). The Earth's magnetic field's vertical component (B) is given as 0.50 * 10⁻⁴ T, and the distance between the left and right side of the car (L) is 1.7 m. Since the motion is horizontal and the magnetic field is vertical, θ is 90 degrees, and sinθ is 1. Using the formula, we can calculate the induced emf (ε) as:

ε = BvLsinθ = 0.50 * 10⁻⁴ T * 20.83 m/s * 1.7 m * sin(90°) = 0.50 * 10⁻⁴ * 20.83 * 1.7 = 1.7755 * 10⁻⁴ V

When we convert this to millivolts by multiplying by 1,000, we get ε = 1.7755 mV. Thus, the induced emf between the left and right side of the car is approximately 1.8 mV, when rounded to one decimal place.

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