Dielectrics and Capacitance Questions and Answers

Answer: C

Multiplying gives \( 10^{-5} \times 100 = 10^{-3} \) coulombs. A millicoulomb is an enormous charge by electrostatic standards, which is why capacitor voltages of a hundred volts are ordinary while a charged sphere at a hundred volts holds almost nothing.

Answer: D

The normal flux density is the same in both, so the field intensity is inversely proportional to the permittivity and is twice as large in the layer of permittivity two. That is where breakdown would begin, other things being equal.

Answer: A

The equivalent electrical thickness of the solid is one millimetre, so the two layers behave as equal capacitances and share the voltage equally: 500 V across one millimetre of air, that is 500 kV/m. Air breaks down at about 3 MV/m, so this gap survives.

Answer: B

The combined capacitance is fifty picofarads and multiplying by two hundred volts gives \( 10^{-8} \) coulombs. Each capacitor carries its own share in proportion to its capacitance, four and six nanocoulombs respectively.

Answer: C

Dividing gives \( 11 \times 10^{3}/(20 \times 10^{6}) = 5.5 \times 10^{-4} \) m. In practice a factor of several times this would be used, to allow for voids, ageing, surges and the reduction of strength with time under stress.

Answer: D

With the charge fixed and the capacitance trebled, the voltage must fall to a third. The stored energy falls to a third as well, the difference having been given up as mechanical work as the slab was drawn into the gap.

Answer: A

With the voltage fixed and the capacitance trebled, the charge must treble too and the source supplies the extra. The stored energy also trebles, and the source in fact delivers twice that increase, half of it being dissipated or done as work.

Answer: B

Capacitance is the ratio of charge to voltage and both rise together, so the ratio is fixed by geometry and permittivity alone. Only if the dielectric is nonlinear, as some ferroelectric ceramics are, does the capacitance depend on the applied voltage.

Answer: C

Correct answer: False, bound charge being unable to move through the dielectric to earth

Bound charge is not free to move: it belongs to molecules held in place, and an earth connection has nothing to conduct. That is exactly what distinguishes it from the free charge on a conductor, which an earth wire removes at once. The bound charge disappears only when the field that produced the polarisation is removed.

Answer: D

It is the normal flux density that is continuous when no free surface charge is present; the field intensity jumps in inverse proportion to the permittivities. The tangential intensity is the component that is always continuous.