Unit 2 Electric Force and Field

Electrostatics

“Net negative” objects have an excess of electrons while “net positive” objects have a deficit in them

Opposite charges attract, like charges repel

Induced separation of charge can attract neutral charges

A net negative object NEARING a neutral object can repel electrons and induce a net positive charge in the nearest region. A net positive object does the opposite and induces a net negative charge in the nearest region.

Methods of Charging:

Charging by friction- Rubbing two objects against each other creates heat that excites electrons and makes them easier to take. The one that’s higher on the electrostatic series will gain the electrons and become net negative while the other becomes net positive (PP7)

Charging by conduction- Conduction or induction causes 2 objects to behave as one and distribute electrons until equilibrium. Ex. a net negative object’s electrons will go into a neutral object to both be net negative. The reverse will happen to a net positive object

Charging by Induction via ground

Electroscopes are devices that indicate if charged. They have 2 leaves on the bottom that are close together when neutral and far apart when similarly charged. They CANNOT attract each other

A ground is a very large conductor that remains neutral even when it loses or receives charge

Case 1- Giving electroscopes a net positive charge via induction. A net negative rod is brought near the scope to kick electrons into the ground. Then the connection to ground is cut and the scope is net positive

Case 2- Giving electroscopes a net negative via induction. A net positive rod is brought near the scope to attract electrons from the ground. Then the connection to the ground is cut and the scope is net negative.

Electric Force

Coulomb’s Law

The magnitude of the electric force between two charges q1 and q2 is (kq1q2)/r² where q1and2 are MAGNITUDES(no negatives) and k is coulomb’s constant (in formula sheet)

Based on Newton’s 3rd Law, the electric forces between 2 charges are equal and opposite even if they have different magnitudes.

You use q² when the two objects are IDENTICAL

You take the average of the charges when they touch AND square it if they’re identical For example, 2 identical spheres one 4 C and the other 0 C(since it’s neutral) would add tg and divide by 2 to make 2 for EACH OBJECT

F_e is inverse squared to r

Fe is directly proportional to q

Electric Field

Vector fields with spheres of influence around central objects.

Electric fields go away from a positive central charge and towards negative central charge

If you place a negative charge in the field then it will go opposite to the electric force

Equations to find the strength of field (units N/C):

Fe/q for when you’re using a small charge in a field

KQ/r² when using a central charge Q and distance from central charge to location P r

Net Electric Force/Field

E= KQ/r²

Fe= (kq1q2)/r²

When you’re trying to calculate net electric field at location P remember that you’re treating P as a positive charge

Use vector conventions (right is positive and left is negative) and make sure the charges are MAGNITUDES in calculations

When a field or force is made around location P and it creates an intermediate direction, find the COMPONENTS of it with appropriate vector conventions.

Models of equal but opposite charges will show arrows leaving and combining with each other. This is ATTRACTION

Models of two like charges will show arrows never meeting but going in the same direction. This is REPULSION

To cancel out a big charge, like say, -16Q, you would have to be far away from it.

Potential difference

Shorter side is negative and longer side is positive in parallel plates

If you place a positive charge in a parallel plate, it will want to “fall” to the negative side, meaning that’s when it has no potential energy. This implies that E_p is highest at the positive side, where they have like charges. The same is true for negative charges as well

Potential difference is the change in electric potential energy per unit charge. Objects only experience the FULL potential difference when they go from plate to plate. They experience none when they go parallel to the plate.

V= E/q where E is the change in ENERGY and NOT THE ELECTRIC FIELD

Whenever a question asks you for the change in electric potential energy you know to use the E=qV and realize that the unit is JOULES and potential energy is a SCALAR

If a particle is slowing down then it is doing negative work

Potential Difference and Electric Field

There are two ways to find the minimum work needed to move a positive particle from a negative plate to a positive one at a CONSTANT VELOCITY

Method 1: Energetics

Since we are using a constant velocity then there is no change in Ek, just Ep. This means that the minimum work equals qV

Method 2: Dynamics

Constant velocity means all forces are balanced so F= qE and therefore W= Fd= qEd

This proves that Electric field= V/d where V is the full potential difference between plates and d is the full perpendicular distance between them. The unit here is V/m

When asked for the electric field of two random points you have to remember that it is CONSTANT. This means you have to do the FULL Difference over the FULL distance to get it for both of them.

Whenever you’re asked for the minimum work to move a particle in vertical plates and you’re given a triangle with distances on them, use the distance that is PERPENDICULAR to the plates.

You could also just divide the distance you want to go by the full distance and multiply by the potential difference to use the qV formula.

We treat the motion of a charge in horizontal plates the same way we treat PARABOLIC MOTION

If the question says that a particle slows down and/or comes to rest then that means the acceleration is NEGATIVE.

When trying to find how close a particle gets to the opposite plate, the distance in your calculation is how much distance the particle COVERS. You have to subtract that distance from the overall distance between the plates to fully answer the question

YOU REMEMBER PARABOLIC MOTION. The viy is ALWAYS ZERO

When using dynamics to find a specific variable, just remember that your dy isn’t the entire distance between parallel plates.

The “velocity that the particle hits the plate” is your LANDING VELOCITY in parabolic motion. This means u have to use vx and vy as a triangle to find the vf and the direction. In these problems, your direction is either above or below the horizontal.

When you’re asked to find the acceleration of an object “knowing the weight is significant”, that means you have to subtract the force of gravity in your Fnet equation from qE.

When trying to find the work done w/ parabolic motion in parallel plates just know that the dy is the distance we use.

Sometimes it’s safer to do dynamics than energetics simply b/c you have more to work with there.

Millikan’s Oil-Drop Experiment

Millikan adjusted the voltage of charged oil droplets in parallel plates until they were “suspended”, meaning that the electric force was equal to the gravitational force. He then found out that the charges were all quantized, meaning they were all multiples of 1.6 × 10^19 C

q= ne describes the elementary charge e times the number of electrons n to get the charge of an object q.

If an oil droplet is accelerating downward at a constant rate LESS than 9.81, then the Fe is still upward but less than Fg. If it is accelerating downward at a constant rate between than 9.81 and 19.62 then the Fe is downward and less than Fg.

When you’re asked to find the acceleration of an object “knowing the weight is significant”, that means you have to subtract the force of gravity in your Fnet equation from qE. You know when you have to do this when it’s an object OTHER than alpha particles, protons, or electrons.

Misconceptions/Mistakes

Glass is an insulator and metal is a conductor. Insulators don’t do shit to charged electroscopes, conductors neutralize them.

REMEMBER THAT CHARGING BY CONDUCTION makes them BOTH CHARGED (net negatives and net negative for ex.)

If a question gives you the force between 2 objects and you have to find the force between one of the objects and another object, use relationships like Fe to r and Fe to q to solve.

REMEMBER THAT ELECTRIC FIELD GOES TOWARD NEGATIVE CENTRAL CHARGES

In a uniform electric field, electric force is CONSTANT

Think about the forces acting on a particle left right up down. Also if they’re alone or not

If you place a negatively charged rod near a neutral magnet and then split it, the side that becomes net negative after the electron ran from the other side got that way through CONDUCTION.

If an electron and a proton are both initially at rest but accelerate across the same parallel plates, then their kinetic energy is the same while their speeds are different.