Explanation

(a)i The charged particle must be in motion or have velocity and the particle's velocity must be inclined to the magnetic field at an angle \(\theta\)

(ii) F = Qv\(\beta\)sin\(\theta\)

(iii) for a charged particle moving parallel to the magnetic field,

\(\theta\) = 0 and F = Qv\(\beta\)sin\(\theta\)

                           F = Qv\(\beta\)sin 0 = 0

Thus, F = 0

(b)The main parts of an electrical transformer are the coil, Soft iron core

(ii) An alternating current in the primary coil produces a changing magnetic field in the primary coil. The changing magnetic field around the core gives rise to a changing magnetic flux linking the secondary coil thereby inducing an alternating e.m.f in the secondary coil as stated in Faraday's law.

c(i) Why the speed of the proton remains constant: The speed of the proton remains constant because the magnetic force acts perpendicular to its velocity, providing centripetal acceleration without doing work on it. This means the force changes the direction of the proton's motion but not its speed, resulting in constant kinetic energy and a uniform speed throughout its circular path.

(ii) I. radius of curved path

qv\(\beta\) = \(\frac{mv^2}{r}\)

r = \(\frac{mv}{q\beta}\)

r = \(\frac{1.7 \times 10^{-27}}{1.6 \times 10^{-19}}\) = 0.24 m.

II. time taken by the proton to move through the magnetic field,

t = \(\frac{\pi r}{2v}\) = \(\frac{3.14 \times 0.24}{2 \times 4.5 \times 10^6}\) = 8.37 x 10\(^{-8}\)s

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