Physics 2011 Jamb Examination

The electric potential \(V\) due to a point charge \(q\) at a distance \(r\) is given by the formula:\[V = \dfrac{q}{4\pi \varepsilon_0 r}\]This follows from the definition of potential as the work done per unit charge in bringing a small positive test charge from infinity to the point in question. The potential decreases inversely with distance from the charge and depends directly on the magnitude of the charge. The constant \(\varepsilon_0\) is the permittivity of free space.

Doping is the deliberate introduction of a small amount of impurity atoms into a pure semiconductor such as germanium or silicon to modify its electrical properties. This process increases charge carrier concentration, producing n-type (excess electrons) or p-type (excess holes) materials. Doping is fundamental in the manufacture of diodes, transistors, and integrated circuits.

The work function \(\phi\) is given by:\[\phi = h f_0\]Substituting the given values:\[\phi = 6.6 × 10^{-34} × 1.3 × 10^{15}\]\[\phi = 8.58 × 10^{-19}\;J\]The work function represents the minimum energy required to eject an electron from the surface of the metal.

In electroplating, the metal to be plated (X) is made the cathode, while the metal used for coating (Y) serves as the anode. The electrolyte contains ions of the coating metal. During electrolysis, metal ions from the anode dissolve into the solution and are deposited on the cathode. Therefore, Y must be the anode to supply ions that plate onto X. A moderate current is used to ensure uniform deposition.

At low pressure, the gas molecules are sufficiently far apart, and when a high potential difference is applied, electrons gain enough energy to ionise the gas atoms. These ions and electrons act as charge carriers, allowing the gas to conduct electricity. Therefore, gases conduct under low pressure and high potential difference.

When inductors are connected in series, the effective inductance is the sum of their individual inductances:\[L_{eq} = 4 + 8 = 12\;H\]The energy stored in an inductor is given by:\[E = \dfrac{1}{2} L I^2\]Substituting the given values:\[E = \dfrac{1}{2} × 12 × 10^2 = 6 × 100 = 600\;J\]However, since none of the provided options equals 600 J, and option C (133 J) is not consistent with the correct calculation, the intended answer likely had a unit or typographical inconsistency. The correct energy stored is 600 J.

Metals have positive temperature coefficients of resistance. As temperature increases, metal atoms vibrate more vigorously, increasing collisions between electrons and atoms. This restricts the flow of electrons, leading to an increase in resistance with temperature.

The relationship between half-life \(t_{1/2}\) and decay constant \(\lambda\) is:\[t_{1/2} = \dfrac{0.693}{\lambda}\]Substituting \(\lambda = 10^{-5}\;s^{-1}\):\[t_{1/2} = \dfrac{0.693}{10^{-5}} = 6.93 × 10^4\;s\]Hence, the half-life is 6.93 × 10⁴ seconds.

For a far-sighted person, the near point is at 50 cm, and the desired near point is 25 cm. The lens should form an image of an object at 25 cm at his near point (50 cm). Using the lens formula:\[\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}\]\[\dfrac{1}{f} = \dfrac{1}{0.50} - \dfrac{1}{0.25} = 2 - 4 = -2\;m^{-1}\]The negative sign shows a virtual image; therefore, the required power is \(P = -2D\). Since none of the options matches this value, no option is correct.

A solar eclipse occurs when the moon moves directly between the Earth and the Sun, blocking all or part of the Sun’s light from reaching the Earth. The moon casts a shadow on the Earth, and observers located within the moon’s umbra see a total eclipse. This alignment happens during the new moon phase, and because the moon’s orbit is slightly tilted, solar eclipses do not occur every month.