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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掳. Answer: The magnetic flux through the circular loop is approximately 0.000307 Tm虏.

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 = 蟺r虏. We are given the radius r = 0.0185 m, so: A = 蟺(0.0185)虏 A 鈮� 0.001076 m虏
02

2. Convert the angle to radians

The angle 胃 is given in degrees, we need to convert it to radians first: 胃 = 13掳 脳 (蟺/180) 胃 鈮� 0.227 radians
03

3. Calculate the magnetic flux through the loop

Now we can calculate the magnetic flux 桅 using the formula: 桅 = B 脳 A 脳 cos(胃) 桅 = (0.29 T) 脳 (0.001076 m虏) 脳 cos(0.227 radians) 桅 鈮� 0.000307 Tm虏 So, the magnetic flux through the circular loop is approximately 0.000307 Tm虏.

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