Magnetic Flux Through a Square Loop

In summary: This is important to consider because it affects the amount of magnetic flux passing through the loop. In summary, the problem involves a loop of wire in the form of a square with sides of 1.50 m, placed at an angle of 40.0° with a uniform magnetic field of 0.95 T. To find the magnetic flux through the loop, the formula Φ = BAcosθ is used, where A represents the area of the loop. The angle θ in the formula represents the angle between the normal of the loop and the magnetic field. It is important to consider this angle because it affects the amount of magnetic flux passing through the loop.
  • #1
ilovejava
21
0

Homework Statement


A loop of wire in the form of a square 1.50 m on each side, its plane makes an angle of 40.0° with a uniform magnetic field of 0.95 T. What is the magnetic flux through the loop?

Homework Equations


Φ = BAcosθ
A = s^2

The Attempt at a Solution


I found the area of the square using A = s^2 which returns 2.25m. Then I just plugged in the values provided in the question making sure to use 40°. I got Φ = 1.64Wb but the answer is 1.37Wb
 
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  • #2
In the formula Φ = BAcosθ, can you describe in words the meaning of the angle θ? What particular angle does it represent?

The angle of 40.0° given in the statement of the problem might not be the angle represented by θ in the formula.
 
  • #3
TSny said:
In the formula Φ = BAcosθ, can you describe in words the meaning of the angle θ? What particular angle does it represent?

The angle of 40.0° given in the statement of the problem might not be the angle represented by θ in the formula.
The angle in the formula is the angle the loop makes with respect to the magnetic field. If the angle was 90 the the magnetic flux would be zero because no magnetic field lines would pass through the loop.
 
  • #4
ilovejava said:
The angle in the formula is the angle the loop makes with respect to the magnetic field. If the angle was 90 the the magnetic flux would be zero because no magnetic field lines would pass through the loop.
θ is not the angle that the plane of the loop makes to the magnetic field.

The picture below shows the case where the plane of the loop makes a 90o angle to the B field.
upload_2017-3-4_17-30-52.png

Would you say that the flux through the loop is zero here?
 
  • #5
TSny said:
θ is not the angle that the plane of the loop makes to the magnetic field.

The picture below shows the case where the plane of the loop makes a 90o angle to the B field.
View attachment 114102
Would you say that the flux through the loop is zero here?
No the flux through the loop is not zero. I guess it's the angle made between the normal of the loop and the magnetic field?
 
  • #6
ilovejava said:
No the flux through the loop is not zero. I guess it's the angle made between the normal of the loop and the magnetic field?
Yes, θ in the formula is the angle between the normal of the loop and the magnetic field.
 

Related to Magnetic Flux Through a Square Loop

1. What is magnetic flux through a square loop?

Magnetic flux through a square loop is a measure of the total amount of magnetic field passing through a square-shaped loop. It is represented by the symbol Φ and is measured in units of webers (Wb).

2. How is magnetic flux through a square loop calculated?

The magnetic flux through a square loop can be calculated by multiplying the strength of the magnetic field (B) by the area of the loop (A) and the cosine of the angle between the magnetic field and the normal to the loop. This can be represented by the equation Φ = BAcosθ.

3. What factors affect the magnetic flux through a square loop?

The magnetic flux through a square loop is affected by the strength of the magnetic field, the area of the loop, and the angle between the magnetic field and the normal to the loop. It is also affected by the material of the loop, as different materials have different magnetic properties.

4. How does changing the angle between the magnetic field and the loop affect the magnetic flux?

Changing the angle between the magnetic field and the loop affects the magnetic flux by changing the value of the cosine in the equation Φ = BAcosθ. As the angle decreases, the value of the cosine increases, resulting in a higher magnetic flux through the loop. Conversely, as the angle increases, the magnetic flux decreases.

5. What is the significance of magnetic flux through a square loop?

The magnetic flux through a square loop is significant because it is a measure of the total amount of magnetic field passing through the loop. It is an important concept in understanding and studying electromagnetism and is used in various applications, such as in motors, generators, and transformers.

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