Electricity and Magnetism - AP Physics 2

To answer this question, we first need to determine what we're looking for that will allow any given light bulb to produce bright light. The answer is power. The more energy that is delivered to the light bulb within a given amount of time, the brighter the light will be. Let's go ahead and look at the equation for power in a circuit.

And since we're told in the question stem that the voltage source is identical in each circuit, we're looking for the circuit that has the largest current.

In order to find which circuit has the largest current, we'll need to invoke Ohm's law.

What this shows is that a higher current will occur in the circuit that has the lowest total resistance. Thus, we'll need to determine what the total resistance is in each of the three circuits.

In circuit A, we can see that there is only a single resistor. Thus, we can give this circuit's total resistance a value of .

In circuit B, we have two resistors that are connected in series. Remember that when resistors are connected in this way, the overall resistance of the circuit increases. We find the total resistance by summing all the resistors connected in series.

Therefore, we can give circuit B a total resistance of .

Now, let's look at circuit C. We can see that there are two resistors connected in parallel, and each of these are connected in series with a third resistor. To solve for the total resistance of this circuit, we first need to determine the equivalent resistance of the two resistors connected in parallel. Once we find that value, then we can take into account the third resistor connected in series.

To solve for the resistance of the two resistors connected in parallel, we have to remember that they add inversely.

Now that we've found the equivalent resistance for the two resistors connected in parallel, we can consider the third resistor connected in series.

Thus, we can give circuit C a value of .

Now that we've found the total resistance for each circuit, we can obtain our answer. Since circuit A has the lowest total resistance, it will also have the greatest current. Consequently, it will also have the greatest power delivered to its resistor (the light bulb), thus causing the light coming from that bulb to be the brightest.

Magnets will align themselves with the surrounding magnetic field. Thus, if the north pole of a magnet is pointing north, the direction of the magnetic field must be pointing north. Magnetic fields point towards magnetic south poles, so the geographic north pole is actually a magnetic south pole.

Charged particles only experience a magnetic force when some component of their velocity is perpendicular to the magnetic field. Here, the velocity is parallel to the magnetic field so the particle does not experience a force.

Since the net charge of the dipole is zero, the net force will also be zero since . The force on the positive charge on top will be directed to the right since positive charge experiences force in the direction of the electric field. For the negative charge on the bottom, the force will be to the left. Both of the forces contribute to a clockwise torque.

The elemental charge is the magnitude of charge, in Coulombs, that each electron or proton has. Because electrons have a negative charge, don't forget to add a negative sign into the equation.

When you convert the answer to microcoulombs, the answer is :

Because we're talking about electrons, the answer must be negative. The way to solve this is to find how many electrons are in 1.5 kg of water. First, we need to convert kilograms of water into grams of water:

Then, we can use the provided molar mass of water to calculate the number of moles of water in 1.5kg of water:

Once we know how many moles of water we have, we can use Avogadro's number () to calculate how many molecules of water are in 83.33mol.

Once we know how many molecules of water we have, we can multiply by 10 to figure out how many electrons those molecules represent, since we are told that each water molecule has 10 electrons.

Finally, we can multiply by the provided charge of an electron to calculate the charge of those electrons.

The equation for the quantity of charge is:

where is the charge quantity, represents the number of electrons, and is the charge of an electron, also known as the elementary charge.

Rewrite the equation.

One coulomb, , consists of electrons,

Substitute these two values into the formula.

This number represents the electron's fundamental charge.

Because this is a neutral balloon, the net charge is equal to the charge the was removed, but opposite in sign. There were 16,000 electrons removed, each of which has a charge of . Therefore, the total charge that was removed is:

To answer the question, we must remember that if that much charge was removed from the balloon, the balloon will now be negative.

Surface area of sphere:

Plug in values:

First, let's calculate the electric field at C due to point A.

We can tell that the net electric field will be in the direction.

in the direction.

Use the equation to find the magnitude of an electric field at a point.

Solve.

Since it is a positive charge, the electric field lines will be pointing away from the charged particle.

We will need to use the electric field equation, twice. Because we are given coordinates, we will need to use vector notation.

Combine the two equations.

Plug in known values.

Note that the charge is positive. This is because the electric field lines point towards the negative charge at the origin, and in order to balance this at your location, the electric field lines of the charge at (0,-3) must be pointing away from the charge.

Potential is not a vector, so we just add up the two potentials and set them to each other. The equation for electric potential is:

If the point we are looking for is distance from , it's from . Cancel all the common terms, then cross-multiply:

Since we had associated with , it's from that charge toward the weaker charge.

Electric field is a vector. In between the charges is where 's field points right and 's field points left, so somewhere in between, the two vectors will add to zero. It will be closer to the weaker charge, , but since field depends on the inverse-square of the distance, it will not be linear, and we'll have to do some math.

First set the magnitudes of the two fields equal to each other. The vectors point in opposite directions, so when their magnitudes are equal, the vector sum is zero.

Many of the terms cancel, making it a bit easier. Now cross multiply and solve the quadratic:

Using coulombs law to solve

Where:

it the first charge, in coulombs.

is the second charge, in coulombs.

is the distance between them, in meters

is the constant of

Converting into

Plugging values into coulombs law

Magnitude will be the absolute value

To solve this problem, we'll need to utilize the equation for the electric force:

We're told that the force each charge experiences is 20 N at a certain distance, but then that distance is doubled. Thus, the new electric force will be:

Use the electric field equation:

Where is

is the charge, in Coulombs

is the distance, in meters.

Convert to and plug in values:

Magnitude is equivalent to absolute value:

Using the electric field equation:

Where is

is the charge, in

is the distance, in .

Convert to and plug in values:

Magnitude is equivalent to absolute value:

Using the electric field equation:

Where is

is the charge, in

is the distance, in .

Convert to and plug in values:

Magnitude is equivalent to absolute value:

Use the electric field equation:

Where is

is the charge, in Coulombs

is the distance, in meters.

Convert to and plug in values:

Magnitude is equivalent to absolute value: