A current I=2 Amperes flows in a circular single loop coil of radius R=10 cm.

(a) Evaluate the magnitude of the magnetic field (in Tesla) at a point P on the axis of the coil, and a distance z=5 cm away from the plane of the coil itself

To find the magnitude of the magnetic field at point P, you can use the Biot-Savart law. The formula is:

B = (μ0 * I * A)/(2 * d),

where:
- B is the magnetic field
- μ0 is the permeability of free space (μ0 = 4π × 10^(-7) T*m/A)
- I is the current
- A is the area of the loop
- d is the distance from the loop to the point P

First, let's calculate the area of the loop. The area of a circle is given by the formula:

A = π * R^2,

where R is the radius of the loop.

Given that the radius, R, is 10 cm, we convert it to meters by dividing by 100:

R = 10 cm = 0.1 m.

Now we can calculate the area:

A = π * (0.1 m)^2 = 0.0314 m^2.

Next, we need to calculate the distance, d, which is the distance from the plane of the coil to point P. In this case, d is given as 5 cm, which is also converted to meters:

d = 5 cm = 0.05 m.

With all the values determined, we can now find the magnetic field at point P using the Biot-Savart law:

B = (μ0 * I * A)/(2 * d).

Plugging in the known values:

B = (4π × 10^(-7) T*m/A * 2 A * 0.0314 m^2)/(2 * 0.05 m).

After simplifying:

B = (2π × 10^(-7) T)/(0.05 m).

B = 40π × 10^(-7) T/m.

Finally, we can approximate the value using the known value for π and the conversion of T/m to T:

B ≈ 40 * 3.14 × 10^(-7) T ≈ 1.26 × 10^(-5) T.

So, the magnitude of the magnetic field at point P is approximately 1.26 × 10^(-5) Tesla.