(a)i State the condition for a charged particle to experience a force in magnetic field
(ii) State the expression for the magnetic force, F acting on a charged particle, Q in a magnetic field of flux density, \(\beta\) with speed, V
(iii) Prove quantitatively that there is no magnetic force moving along the direction of a magnetic field.
(b)i Mention the main parts of an electrical transformer.
(ii) Explain how an alternating potential difference applied to the primary coil gives rise to an induced e.m.f in the secondary coil of a transformer.
(c) Proton of mass 1.7 x 10(^{-27}\) kg enters a magnetic field of flux density 0.207 normally and followed a quarter circle path before existing with a constant speed of 4.5 x 10\(^6\)m/s
(i) Explain why the speed of the proton remains constant.
(ii) Calculate the
I. radius of the circular path
II. time taken by the proton to move through the magnetic field [e = 1.6 x 10\(^{-19}\) C, \(\pi\) = 3.14]
(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
(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
