Magnetic flux and magnetic field at a point are related concepts in electromagnetism, but they are fundamentally different. Below is the concise differentiation:
| Magnetic Flux | Magnetic Field at a Point |
|---|---|
| Scalar quantity | Vector quantity |
| \( \Phi_B = B A \cos \theta \) | \( \mathbf{B} = \frac{F}{qv} \) |
| Measured in Weber (Wb) | Measured in Tesla (T) |
| Depends on area | Depends on current and distance |
| Total number of field lines through a surface | Local property of space at a point |
In summary, magnetic flux is the total magnetic field passing through a given area, while the magnetic field at a point refers to the local magnetic influence at a specific point in space.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).