A solenoid of length 10 cm has 247 turns and a magnetic field at the center of 1.2 T. What is the current through the solenoid?

386.6 A

Explanation:

We are given;

Solenoid length; L = 10 cm = 0.1 m

Number of turns; N = 247

Magnetic field; B = 1.2 T

Now, at the centre of a long solenoid of N turns/metre carrying a current(I), the formula for the magnetic field is given as;

B = μ_oNI/L

Making I the subject we have;

I = BL/μ_oN

Where μ_o is the vacuum of permeability and has a constant value of 4π × 10^(−7) H/m

Thus;

I = (1.2 × 0.1)/(4π × 10^(−7) × 247)

I = 386.6 A

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 .