Try the fastest way to create flashcards
Question

# A uniform flux density of 1 T is perpendicular to the plane of a five-turn circular coil of radius 10 cm. Find the flux linking the coil and the flux linkages. Suppose that the field is decreased to zero at a uniform rate in 1 ms. Find the magnitude of the voltage induced in the coil.

Solution

Verified
Step 1
1 of 3

From problem description we have:

$B = 1 \ \frac{\text{Wb}}{\text{m}^2}, \ r =10 \ \text{cm} = 0.1 \ \text{m}, \ \text{N} = 5 \ \text{turns}, \ \Delta t = 1 \ \text{ms}$

Notice that flux density $B$ is perpendicular to the surface $A$ surrounded by the coil. The magnetic flux passing through surface $A$ is:

$\phi = B \cdot A = B \cdot r^2 \pi = 1 \ \frac{\text{Wb}}{\text{m}^2} \cdot 0.1^2 \ \text{m}^2 \cdot \pi = \boxed{0.0314 \ \text{Wb}}$

The flux linkages we can determ as follows:

$\lambda = \text{N} \cdot \phi = 5 \ \text{turns} \cdot 0.0314 \ \text{Wb} = \boxed{0,157 \ \text{Wb} \cdot \text{turns}}$

## Recommended textbook solutions

#### Fundamentals of Electric Circuits

6th EditionISBN: 9780078028229 (2 more)Charles Alexander, Matthew Sadiku
2,120 solutions

#### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th EditionISBN: 9780133942651 (8 more)Randall D. Knight
3,508 solutions

#### Electrical Engineering: Principles and Applications

7th EditionISBN: 9780134484143 (2 more)Allan R. Hambley
1,451 solutions