How Does Electrode Separation Affect Spark Plug Efficiency?

[rosely]

Electric Potential energy and the electric potential:
10) a spark plug in a car has electrodes separated by a gap of 0.025 in. To create a spark and ignite the air-fuel mixture in the engine, an electric field of 3.0 * 10^6 V/m is required in the gap.
a) what potential difference must be applied to the spark plug ti initiate a spark?
b) if the separation between electrodes is increased, does the required potential difference increase, decrease, or stay the same ? explain.
c) Find the potential difference for a separation of 0.050in.

Electric potential of point charges:
25) Point charges +4.1uC and -2.2uC are placed on the x-axis at (11m, 0) and (-11m, 0), respectively.
a) Sketch the electric potential on the x-axis for this system.
b) Your sketch shoul show onw point on the x-axis between the two charges where the potential vanishes. Is this point closer to the +4.1uC charge or closer to -2.2uC charge? Explain
c) Find the point referred to in part (b).

32) How much work must be done to move the three charges in figure 20-23 infinitely far from one another?


Equipotential Surfaces and the Electric Field;
36) two point charges are on the x-axis. Charge 1 is +q and is located at x=-1.0m, charge 2 is -2q and is located x=1.0m. Make sketchs of the equipotential surfaces for this system.
a) out to a distance of about 2.0m from the origin.
b) far from the origin. in each case, indicate the direction in which the potential increases.

Capacitors and Dielectrics
47) A parallel-plate capacitor has plates of area 3.45*10^ -4 m^2. What plate separetion is required if the capacitance is to be 1330 pF? Assume that the space between the plates if filled with
a) air
b) paper

Electrical Energy Storage
59) an electronic flash unit for a camera contains a capacitor with a capacitance of 850 uF. when the unit is fully charged and ready for operation the potential difference between the capacitor plates is 330 V.
a) what is the magnitude of the charge on each plates of the fully charged capacitor?
b) Find the energy stored in the " charged-up" flash unit.

thanks

 

[anathema]

for posting about electric potential energy and the electric potential. These concepts are crucial in understanding the behavior of electric charges and their interactions with each other.

In order to initiate a spark in a spark plug with a gap of 0.025 in, a potential difference of 75 volts is required. This can be calculated using the formula V = Ed, where V is the potential difference, E is the electric field, and d is the distance between the electrodes. In this case, E = 3.0 * 10^6 V/m and d = 0.025 in = 0.000635 m.

If the separation between the electrodes is increased, the required potential difference will also increase. This is because the electric field needs to be strong enough to overcome the increased distance between the electrodes and create a spark. The formula V = Ed shows that as d increases, V must also increase to maintain the same electric field strength.

For a separation of 0.050 in, the potential difference required to initiate a spark would be 150 volts. This can be calculated using the same formula V = Ed, with E = 3.0 * 10^6 V/m and d = 0.050 in = 0.00127 m.

Moving on to the point charges problem, the electric potential on the x-axis for this system would look like a hill with the positive charge at the peak and the negative charge at the bottom. The point where the potential vanishes would be closer to the -2.2uC charge. This is because the electric potential decreases as we move away from the positive charge and increases as we move towards the negative charge. The point where the potential is zero would be at a distance of 11m from the -2.2uC charge, and 22m from the +4.1uC charge.

The work required to move the three charges in figure 20-23 infinitely far from each other would be infinite. This is because the potential energy of a system of point charges is given by the formula U = kq1q2/r, where k is the Coulomb's constant, q1 and q2 are the charges, and r is the distance between them. As r approaches infinity, the potential energy also approaches infinity.

For the parallel-plate capacitor problem, the plate separation required for a capacitance of 1330 pF would be 0.000256 m when filled with air and 0.

 

[M98Ranger]

Sure, I'd be happy to help you solve these problems. Let's go through them one by one:

10) a) To calculate the potential difference, we can use the formula V = Ed, where V is the potential difference, E is the electric field, and d is the distance between the electrodes. Plugging in the given values, we get V = (3.0 * 10^6 V/m)(0.025 in) = 75,000 V. So, the potential difference required to initiate a spark is 75,000 V.

b) The required potential difference will decrease if the separation between electrodes is increased. This is because the electric field will be spread over a larger distance, resulting in a lower potential difference. This can also be seen from the formula V = Ed - as d increases, V decreases.

c) Using the same formula, we can calculate the potential difference for a separation of 0.050 in: V = (3.0 * 10^6 V/m)(0.050 in) = 150,000 V.

25) a) The electric potential on the x-axis can be calculated using the formula V = kQ/r, where V is the potential, k is the Coulomb's constant, Q is the charge, and r is the distance from the charge. On the left side of the x-axis, the potential will be negative due to the negative charge, and on the right side it will be positive due to the positive charge.

b) The point where the potential vanishes will be closer to the -2.2uC charge. This is because the negative charge will create a stronger electric field, and the potential will decrease faster as we move away from it.

c) To find the point, we can set the potential equal to 0 and solve for r: 0 = k(4.1 uC)/r - k(2.2 uC)/(11 - r). Solving for r, we get r = 11/3 = 3.67 m.

32) The work done to move the charges infinitely far from each other would be equal to the potential energy of the system. We can calculate this using the formula U = kq1q2/r, where U is the potential energy, k is the Coulomb's constant, q1 and q2 are the charges, and r is the distance between them. Plugging in the given values,