A5.0-cm by 7.0-cm rectangular coil has 100 turns. its axis makes an angle of 65° with a uniform magnetic field of 0.55 t. what is the magnetic flux through this coil?

0.0814 Wb

Explanation:

L = length of the rectangular coil = 5 cm = 0.05 m

w = width of rectangular coil = 7 cm = 0.07 m

A = Area of the coil = L w = 0.05 x 0.07 = 35 x 10⁻⁴ m²

B = magnitude of uniform magnetic field = 0.55 T

θ = angle of axis of coil with magnetic field = 65°

Magnetic flux through the coil is given as

Φ = N B A Cosθ

Φ = (100) (0.55) (35 x 10⁻⁴ ) Cos65

Φ = 0.0814 Wb

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .