Question

The solenoid is made up of 7 turns and it has a radius of 1,5 m. The strength of the magnetic field is 3,3 T. The magnetic flux through the solenoid is 6,04 Wb.

Find the angle between the magnetic field and the normal to the coil.

INSTRUCTION: Round your answer to two decimal places.

Answer 1

To find the angle between the magnetic field and the normal to the coil, we can use the formula for magnetic flux:

\[
\Phi = B A \cos(\theta)
\]

where:
- \(\Phi\) is the magnetic flux (in webers, Wb),
- \(B\) is the magnetic field strength (in teslas, T),
- \(A\) is the area of the coil (in square meters, m²),
- \(\theta\) is the angle between the magnetic field and the normal to the coil (in degrees or radians).

### Step 1: Calculate the Area of the Coil

The area \(A\) of the circular coil can be calculated using the formula:

\[
A = \pi r^2
\]

Given that the radius \(r = 1.5 \, m\):

\[
A = \pi (1.5)^2 = \pi \cdot 2.25 \approx 7.06858 \, m^2
\]

### Step 2: Rearranging the Flux Equation

We can rearrange the magnetic flux formula to solve for \(\cos(\theta)\):

\[
\cos(\theta) = \frac{\Phi}{B \cdot A}
\]

### Step 3: Substitute the Known Values

Now, substitute \(\Phi = 6.04 \, Wb\), \(B = 3.3 \, T\), and \(A \approx 7.06858 \, m^2\):

\[
\cos(\theta) = \frac{6.04}{3.3 \cdot 7.06858}
\]

Calculating the denominator:

\[
3.3 \cdot 7.06858 \approx 23.327
\]

Now substitute this value into the equation:

\[
\cos(\theta) = \frac{6.04}{23.327} \approx 0.259
\]

### Step 4: Finding the Angle

Now we can use the inverse cosine function to find \(\theta\):

\[
\theta = \cos^{-1}(0.259)
\]

Calculating this gives:

\[
\theta \approx 75.3^\circ
\]

### Final Answer

Rounding to two decimal places, the angle \(\theta\) between the magnetic field and the normal to the coil is:

\[
\theta \approx 75.30^\circ
\]