Electric Potential Homework: 3000V Needed for 0.1cm Spark

[lha08]

Homework Statement

The gap in the spark plug of the car is 0.1 cm. What potential difference is needed to produce a spark given that the breakdown strength of air is 3X10^6 V/m.

Homework Equations

The Attempt at a Solution

I'm sort of confused by what they're asking...like i tried using the formula V= -Ed but then apparently in the answers, it says 'for 1 m, voltage difference is 3X10^6 V. For 0.1 cm, voltage difference is 0.001 X (3X10^6)= 3000V.
I don't understand why do we need to compare it to 1 m and why when they calculated it, they didn't place a negative sign like in the formula...

 

[Doc Al]

I don't understand why do we need to compare it to 1 m and why when they calculated it,

They are just trying to explain the meaning of the formula. The electric field is given as XXX volts/meter, so the voltage difference is proportional to the distance. It's equivalent to just using the formula.

they didn't place a negative sign like in the formula...

All they want is the magnitude of the potential difference. The sign of the potential difference depends on the direction of the field, which is not given.

 

[lha08]

They are just trying to explain the meaning of the formula. The electric field is given as XXX volts/meter, so the voltage difference is proportional to the distance. It's equivalent to just using the formula.

All they want is the magnitude of the potential difference. The sign of the potential difference depends on the direction of the field, which is not given.

I'm noticing that when I'm doing problems and they ask for the change in electric potential, for some reason, they are always taking the magnitude while I'm always adding a positive or negative sign..like for example, when an electron is moving with the field (its negative work) but then I thought that the potential should also be negative since it's losing potential energy...but its not...is there any particular reason as to why this is?

 

[Doc Al]

like for example, when an electron is moving with the field (its negative work) but then I thought that the potential should also be negative since it's losing potential energy...but its not...is there any particular reason as to why this is?

Don't confuse potential with potential energy. An electron is negative, so its potential energy decreases as it moves in the direction of the field even though the potential is increasing.