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?

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

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.

SolutionThe 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