## Related questions with answers

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

VerifiedFrom 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:

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

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