The equivalent capacitance of two capacitors in parallel is simply the sum of the two capacitors, so =
- = 2C. The ratio between the equivalent capacitance of the two capacitors in series and the two
capacitors in parallel is therefore:
- C
The energy stored in a capacitor is. When a dielectric with a dielectric constant of is
inserted between the plates of a capacitor with capacitance C, the new capacitance is C. So (C) is the
correct answer.
- D
When the dielectric is inserted, the electrons in it create an electric field that opposes the field between the
plates of the capacitor. Since electric field and potential difference are directly proportional, this decrease in
the electric field causes a decrease in the potential difference.
The energy stored in a capacitor is given by the equation , so a decrease in the potential
difference also leads to a decrease in the stored energy.
Magnetism
WHEN WE THINK “MAGNET,” WE MIGHT envision those things we stick on our fridge
door. It may be a bit confusing, then, to discover that magnetism is closely related to
electricity. In fact, there is a single force—the electromagnetic force—that governs the
behavior of both magnets and electric charges.
We have seen that there is a reciprocal relationship between electric charges and electric
fields: electric charges generate electric fields and electric fields exert a force on electric
charges. Similarly, there is a reciprocal relationship between a moving electric charge and
a magnetic field: a moving electric charge creates a magnetic field, and magnetic fields
exert a force on moving charges.
Bearing this reciprocal relationship in mind, we can make sense of electromagnets, the
on-off magnets you see, for instance, lifting and dropping cars at the junkyard. The
magnetism in these electromagnets is generated by a current running through the magnet
that can be turned on and off at will. However, we still haven’t explained how any of this
connects with the permanent magnets we stick to our fridge door.