A beam of electrons moves at right angles to a magnetic field of 4.5 × 10-2 tesla. If the electrons have a velocity of 6.5 × 106 meters/second, what is the force acting on the electrons? The value of q = -1.6 × 10-19 coulombs.
A.
-2.9 × 106 N
B.
-3.9 × 10-14 N
C.
-4.9 × 10-14 N
D.
-6.5 × 10-13 N
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Capacitors: devices for storing charge
A capacitor is a device for storing charge. It is usually made up of two plates separated by a thin insulating material known as the dielectric. One plate of the capacitor is positively charged, while the other has negative charge.
The charge stored in a capacitor is proportional to the potential difference between the two plates. For a capacitor with charge Q on the positive plate and -Q on the negative plate, the charge is proportional to the potential:
If C is the capacitance, Q = CV
The capacitance is a measure of the amount of charge a capacitor can store; this is determined by the capacitor geometry and by the kind of dielectric between the plates. For a parallel plate capacitor made up of two plates of area A and separated by a distance d, with no dielectric material, the capacitance is given by :

Note that capacitance has units of farads (F). A 1 F capacitor is
exceptionally large; typical capacitors have capacitances in the pF -
microfarad range.
Dielectrics, insulating materials placed between the plates of
a capacitor, cause the electric field inside the capacitor to be
reduced for the same amount of charge on the plates. This is because
the molecules of the dielectric material get polarized in the field,
and they align themselves in a way that sets up another field inside
the dielectric opposite to the field from the capacitor plates. The
dielectric constant is the ratio of the electric field without the
dielectric to the field with the dielectric:


Note that for a set of parallel plates, the electric field between
the plates is related to the potential difference by the equation:
for a parallel-plate capacitor: E = V / d
For a given potential difference (i.e., for a given voltage),
the higher the dielectric constant, the more charge can be stored in
the capacitor. For a parallel-plate capacitor with a dielectric between
the plates, the capacitance is:

Energy stored in a capacitor
The energy stored in a capacitor is the same as the work needed to build up the charge on the plates. As the charge increases, the harder it is to add more. Potential energy is the charge multiplied by the potential, and as the charge builds up the potential does too. If the potential difference between the two plates is V at the end of the process, and 0 at the start, the average potential is V / 2. Multiplying this average potential by the charge gives the potential energy : PE = 1/2 Q V.
Substituting in for Q, Q = CV, gives:
The energy stored in a capacitor is: U = 1/2 C V2
Capacitors have a variety of uses because there are many applications that involve storing charge. A good example is computer memory, but capacitors are found in all sorts of electrical circuits, and are often used to minimize voltage fluctuations. Another application is a flash bulb for a camera, which requires a lot of charge to be transferred in a short time. Batteries are good at providing a small amount of charge for a long time, so charge is transferred slowly from a battery to a capacitor. The capacitor is discharged quickly through a flash bulb, lighting the bulb brightly for a short time.
If the distance between the plates of a capacitor is changed, the capacitance is changed. For a charged capacitor, a change in capacitance correspond to a change in voltage, which is easily measured. This is exploited in applications ranging from certain microphones to the the keys in some computer keyboards.
A capacitor is a device for storing charge. It is usually made up of two plates separated by a thin insulating material known as the dielectric. One plate of the capacitor is positively charged, while the other has negative charge.
The charge stored in a capacitor is proportional to the potential difference between the two plates. For a capacitor with charge Q on the positive plate and -Q on the negative plate, the charge is proportional to the potential:
If C is the capacitance, Q = CV
The capacitance is a measure of the amount of charge a capacitor can store; this is determined by the capacitor geometry and by the kind of dielectric between the plates. For a parallel plate capacitor made up of two plates of area A and separated by a distance d, with no dielectric material, the capacitance is given by :

Note that capacitance has units of farads (F). A 1 F capacitor is
exceptionally large; typical capacitors have capacitances in the pF -
microfarad range.
Dielectrics, insulating materials placed between the plates of
a capacitor, cause the electric field inside the capacitor to be
reduced for the same amount of charge on the plates. This is because
the molecules of the dielectric material get polarized in the field,
and they align themselves in a way that sets up another field inside
the dielectric opposite to the field from the capacitor plates. The
dielectric constant is the ratio of the electric field without the
dielectric to the field with the dielectric:


Note that for a set of parallel plates, the electric field between
the plates is related to the potential difference by the equation:
for a parallel-plate capacitor: E = V / d
For a given potential difference (i.e., for a given voltage),
the higher the dielectric constant, the more charge can be stored in
the capacitor. For a parallel-plate capacitor with a dielectric between
the plates, the capacitance is:

Energy stored in a capacitor
The energy stored in a capacitor is the same as the work needed to build up the charge on the plates. As the charge increases, the harder it is to add more. Potential energy is the charge multiplied by the potential, and as the charge builds up the potential does too. If the potential difference between the two plates is V at the end of the process, and 0 at the start, the average potential is V / 2. Multiplying this average potential by the charge gives the potential energy : PE = 1/2 Q V.
Substituting in for Q, Q = CV, gives:
The energy stored in a capacitor is: U = 1/2 C V2
Capacitors have a variety of uses because there are many applications that involve storing charge. A good example is computer memory, but capacitors are found in all sorts of electrical circuits, and are often used to minimize voltage fluctuations. Another application is a flash bulb for a camera, which requires a lot of charge to be transferred in a short time. Batteries are good at providing a small amount of charge for a long time, so charge is transferred slowly from a battery to a capacitor. The capacitor is discharged quickly through a flash bulb, lighting the bulb brightly for a short time.
If the distance between the plates of a capacitor is changed, the capacitance is changed. For a charged capacitor, a change in capacitance correspond to a change in voltage, which is easily measured. This is exploited in applications ranging from certain microphones to the the keys in some computer keyboards.
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