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Chapter 20: Problem 75

A uniform magnetic field of magnitude 0.29 T makes an angle of \(13^{\circ}\) with the plane of a circular loop of wire. The loop has radius $1.85 \mathrm{cm} .$ What is the magnetic flux through the loop?

Short Answer

Expert verified
Question: Calculate the magnetic flux through a circular loop of wire with a radius of 1.85 cm, placed in a uniform magnetic field of 0.29 T. The angle between the magnetic field and the plane of the loop is 13°. Answer: The magnetic flux through the circular loop is approximately 0.000307 Tm².

Step by step solution

01

1. Calculate the area of the circular loop

The area A of the circular loop can be calculated using the formula A = πr². We are given the radius r = 0.0185 m, so: A = π(0.0185)² A ≈ 0.001076 m²
02

2. Convert the angle to radians

The angle θ is given in degrees, we need to convert it to radians first: θ = 13° × (π/180) θ ≈ 0.227 radians
03

3. Calculate the magnetic flux through the loop

Now we can calculate the magnetic flux Φ using the formula: Φ = B × A × cos(θ) Φ = (0.29 T) × (0.001076 m²) × cos(0.227 radians) Φ ≈ 0.000307 Tm² So, the magnetic flux through the circular loop is approximately 0.000307 Tm².

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