If the Earth’s field (5.0×10−5 T) points north with a dip angle of 38∘, which direction(s) will the car be moving to produce the maximum emf

Question

If the Earth’s field (5.0×10−5 T) points north with a dip angle of 38∘, which direction(s) will the car be moving to produce the maximum emf induced in the antenna?

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Gerda 4 years 2021-09-05T03:20:50+00:00 1 Answers 55 views 0

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  1. Cherry
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    2021-09-05T03:22:21+00:00
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    Answer:

    a. the car moves 90° to the north in the east-west direction b. 0.61 mV

    Explanation:

    Here is the complete question

    When a car drives through the Earth’s magnetic field, an emf is induced in its vertical 55-cm-longradio antenna.

    Part A

    If the Earth’s field (5.0×10−5 T) points north with a dip angle of 38∘, which direction(s) will the car be moving to produce the maximum emf induced in the antenna?

    Part B

    What is the maximum emf induced in the antenna? The car’s speed is 22.0 m/s on a horizontal road.

    Express your answer to two significant figures and include the appropriate units.

    Solution

    The induced emf E = -dBAcosθ/dt . where B is the earth’s magnetic field strength and A the area the field passes through. The induced emf is maximum when the angle between the field and the area is zero. That is cosθ = 0 ⇒ θ = 90°. Thus the car moves 90° to the north in the east-west direction.

    b. The induced emf E = BLVsinθ where B = magnetic field strength = 5.0 10⁻⁵ T, L = length of antenna = 55 cm = 0.55 m and V = velocity of car = 22 m/s, θ = angle between the north and the field = 38°.

    So, E = 5.0 10⁻⁵ T × 0.55 m × 22 m/s sin38 = 0.605 × 10⁻³ V = 0.61 mV

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