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AP Physics 2 : Electric Force Between Point Charges

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Example Question #1 : Electric Force Between Point Charges

Two charges are placed a certain distance apart such that the force that each charge experiences is 20 N. If the distance between the charges is doubled, what is the new force that each charge experiences?

Possible Answers:

80N

40N

10N

There is no way to determine the new force

Correct answer:

Explanation:

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

$F_{e}=k\frac{Q_{1}Q_{2}}{r^{2}}$

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:

$F_{e}^{'}=k\frac{Q_{1}Q_{2}}{(2r)^{2}}=k\frac{Q_{1}Q_{2}}{4r^{2}}=\frac{F_{e}}{4}=\frac{20N}{4}=5N$

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Example Question #1 : Electric Force Between Point Charges

What is the force experienced by a $20\mu C$ point charge away from a $30\mu C$ point charge?

Possible Answers:

The point charge experiences no force

0.216N

0.108N

1.08N

5.4N

Correct answer:

0.216N

Explanation:

The equation to find the force from two point charges is called Coulomb's Law.

$F=\frac{kq_1q_2}{r^2}$

In this equation, is force in Newtons, is the respective charge value in $\mu C$ , is radius in meters, and is the Coulomb constant, which has a value of $9 \cdot 10^9 \frac{N*m^2}{C^2}$ .

Now, we just plug in the numbers. Note: the charge values are in microcoulombs (the Greek letter $\mu$ , called "mu," stands for micro), which is equal to $10^{-6}$ .

$F&=\frac{kq_1q_2}{r^2}$

$F=\frac{(9\cdot 10^9\frac{N*m^2}{C^2}) \cdot (20\cdot 10^{-6}\mu C) \cdot (30 \cdot 10^{-6}\mu C)}{(5m)^2}$

F= 0.216

Therefore, the force experienced on either charge is 0.216N of force.

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Example Question #1 : Electric Force Between Point Charges

You have two point charges, q_1 and q_2 , 3m away from each other. The value of q_1 is $3\mu C$ , and the force they both experience is 0.024 N . What is the value of q_2 ?

$k=9\cdot 10^9\frac{N\cdot m^2}{C^2}$

Possible Answers:

$12\mu C$

$6\mu C$

$16\mu C$

$5\mu C$

$8\mu C$

Correct answer:

$8\mu C$

Explanation:

The equation for the force between two point charges is as follows:

$F=\frac{kq_1q_2}{r^2}$

We have the values for , q_1 , , and , so we just need to rearrange the equation to solve for q_2 , then plug in the values we have.

$q_2=\frac{F\cdot r^2}{k\cdot q_1}$

$q_2= \frac{0.024 \cdot 3^2}{(9\cdot 10^9)\cdot (3\cdot 10^{-6})}$

$q_2= 8\cdot 10^{-6}$

Therefore, the value for the second charge is $8\mu C$ .

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Example Question #4 : Electric Force Between Point Charges

Two objects in space are placed 35m apart. One has a charge of 90e , the second has a charge of -95e . What is the electric force between them?

Possible Answers:

$1.6\cdot 10^{-27}N$ away from each other

$3.75\cdot 10^{-27}N$ away from each other

$3.75\cdot 10^{-27}N$ towards each other

$1.6\cdot 10^{27}N$ towards each other

$1.6\cdot 10^{-27}N$ towards each other

Correct answer:

$1.6\cdot 10^{-27}N$ towards each other

Explanation:

Use Coloumb's law:

$E_{force}=\frac{kq_1q_2}{r^2}$

First, convert the charges into coulombs.

$1 e = 1.6\cdot 10^{-19} C$

$q_1=1.44\cdot 10^{-17}C$

$q_2=-1.52\cdot 10^{-17}$

Plug in values into Coulomb's law.

$E_{force}=9\cdot10^{9}\frac{N\cdot m^{2}}{C^{2}}\cdot \frac{(1.44\cdot10^{-17}C)(-1.52\cdot10^{-17}C)}{(35m)^{2}}$

$E_{force}=-1.6\cdot 10^{-27}N$

Negative electric forces indicate attractive forces. Alternatively, we can reason that since one charge is positive, and the other is negative, the charges will attract.

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Example Question #1 : Electric Force Between Point Charges

Coloumbs law for varsity

If charge has a value of $-9*10^{-13}C$ , and charge has a value of $8*10^{-13}C$ , and the distance between their centers, , is 23 cm what will be the magnitude of the force on charge ?

Possible Answers:

$|F|=1.22*10^{-13}N$

None of these

$|F|=2.33*10^{-13}N$

$|F|=4.22*10^{-13}N$

$|F|=1.84*10^{-13}N$

Correct answer:

$|F|=1.22*10^{-13}N$

Explanation:

Using coulombs law to solve

$F=k\frac{q_1q_2}{r^2}$

Where:

q_1 it the first charge, in coulombs.

q_2 is the second charge, in coulombs.

is the distance between them, in meters

is the constant of $9*10^9\frac{N*m^2}{C^2}$

Converting into

$23cm*\frac{1m}{100cm}=.23m$

Plugging values into coulombs law

$F=9*10^{9}\frac{-9*10^{-13}8*10^{-13}}{.23^2}$

$F=-1.22*10^{-13}N$

The magnitude will be the absolute value.

$|F|=1.22*10^{-13}N$

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Example Question #6 : Electric Force Between Point Charges

Coloumbs law for varsity

If charge has a value of $-9*10^{-13}C$ , and charge has a value of $8*10^{-13}C$ , and the distance between their centers, , has a value of 66 cm , what will be the force on charge ?

Possible Answers:

$|F|=1.49*10^{-14}N$

|F|=1.49N

$|F|=2.22*10^{-14}N$

None of these

$|F|=3.75*10^{-14}N$

Correct answer:

$|F|=1.49*10^{-14}N$

Explanation:

Using coulombs law to solve

$F=k\frac{q_1q_2}{r^2}$

Where:

q_1 it the first charge, in coulombs.

q_2 is the second charge, in coulombs.

is the distance between them, in meters

is the constant of $9*10^9\frac{N*m^2}{C^2}$

Converting into

$66cm*\frac{1m}{100cm}=.66m$

Plugging values into coulombs law

$F=9*10^9\frac{(-9*10^{-13})(8*10^{-13})}{{.66}^2}$

$F=-1.49*10^{-14}N$

Magnitude will be the absolute value

$|F|=1.49*10^{-14}N$

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Example Question #7 : Electric Force Between Point Charges

Coloumbs law for varsity

Charge has a charge of 9 nC

Charge has a charge of -2nC

The distance between their centers, is 5.5 mm .

What is the magnitude of the force on due to ?

Possible Answers:

$|\overrightarrow{F}|=2.59*10^{-3}N$

$|\overrightarrow{F}|=5.35*10^{-3}N$

$|\overrightarrow{F}|=9.87*10^{-3}N$

$|\overrightarrow{F}|=1.89*10^{-3}N$

None of these

Correct answer:

$|\overrightarrow{F}|=5.35*10^{-3}N$

Explanation:

Using the electric field equation:

$\overrightarrow{E}=k\frac{q_A q_B}{r^2}$

Where is $9.0*10^9 N\frac{m^2}{C^2}$

q_A is charge , in coulombs

q_B is charge , in coulombs

is the distance, in meters .

Convert to and plug in values:

$\overrightarrow{F}=9.0*10^9\frac{9*10^{-9}*-2*10^{-9}}{.025^2}$

$\overrightarrow{F}=-5.35*10^{-3}{N}$

Magnitude is equivalent to absolute value:

$|\overrightarrow{F}|=5.35*10^{-3}N$

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Example Question #1 : Electric Force Between Point Charges

Coloumbs law for varsity

Charge has a charge of 10 nC

Charge has a charge of 20nC

The distance between their centers, is 15 cm .

What is the magnitude of the force on due to ?

Possible Answers:

$|\overrightarrow{F}|=3*10^{-5}{N}$

$|\overrightarrow{F}|=6.9*10^{-5}{N}$

None of these

$|\overrightarrow{F}|=4*10^{-5}{N}$

$|\overrightarrow{F}|=8*10^{-5}{N}$

Correct answer:

$|\overrightarrow{F}|=8*10^{-5}{N}$

Explanation:

Use Coulomb's law:

$\overrightarrow{E}=k\frac{q_A q_B}{r^2}$

Where is $9.0*10^9 N\frac{m^2}{C^2}$

q_A is charge , in coulombs

q_B is charge , in coulombs

is the distance, in meters .

Convert to and plug in values:

$\overrightarrow{F}=9.0*10^9\frac{20*10^{-9}*10*10^{-9}}{.15^2}$

$\overrightarrow{F}=8*10^{-5}{N}$

Magnitude is equivalent to absolute value:

$|\overrightarrow{F}|=8*10^{-5}{N}$

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Example Question #1 : Electric Force Between Point Charges

Coloumbs law for varsity

Charge has a charge of 8 nC

Charge has a charge of 10nC

The distance between their centers, is 1.0 mm .

Determine the magnitude of the electric force on due to .

Possible Answers:

$|\overrightarrow{F}|=4.2*10^{-1}{N}$

None of these

$|\overrightarrow{F}|=7.2*10^{-9}{N}$

$|\overrightarrow{F}|=3.7*10^{-1}{N}$

$|\overrightarrow{F}|=7.2*10^{-1}{N}$

Correct answer:

$|\overrightarrow{F}|=7.2*10^{-1}{N}$

Explanation:

Use Coulomb's law:

$\overrightarrow{E}=k\frac{q_A q_B}{r^2}$

Where is $9.0*10^9 N\frac{m^2}{C^2}$

q_A is charge , in coulombs

q_B is charge , in coulombs

is the distance, in meters .

Convert to and plug in values:

$\overrightarrow{F}=9.0*10^9\frac{8*10^{-9}*10*10^{-9}}{.001^2}$

$\overrightarrow{F}=7.2*10^{-1}{N}$

Magnitude is equivalent to absolute value:

$|\overrightarrow{F}|=7.2*10^{-1}{N}$

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Example Question #1 : Electric Force Between Point Charges

Coloumbs law for varsity

Charge has a charge of 19 nC

Charge has a charge of -28nC

The distance between their centers, is 4.5 mm .

What is the magnitude of the force on due to ?

Possible Answers:

None of these

$|\overrightarrow{F}|=7.9*10^{-1}{N}$

$|\overrightarrow{F}|=4.5*10^{-1}{N}$

$|\overrightarrow{F}|=9.1*10^{-1}{N}$

$|\overrightarrow{F}|=2.4*10^{-1}{N}$

Correct answer:

$|\overrightarrow{F}|=2.4*10^{-1}{N}$

Explanation:

Use Coulomb's law:

$\overrightarrow{E}=k\frac{q_A q_B}{r^2}$

Where is $9.0*10^9 N\frac{m^2}{C^2}$

q_A is charge , in Coulombs

q_B is charge , in Coulombs

is the distance, in meters.

Convert to and plug in values:

$\overrightarrow{F}=9.0*10^9\frac{19*10^{-9}*-28*10^{-9}}{.0045^2}$

$\overrightarrow{F}=-2.4*10^{-1}{N}$

Magnitude is equivalent to absolute value:

$|\overrightarrow{F}|=2.4*10^{-1}{N}$

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AP Physics 2 : Electric Force Between Point Charges

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Example Questions

Example Question #1 : Electric Force Between Point Charges

Example Question #1 : Electric Force Between Point Charges

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Example Question #1 : Electric Force Between Point Charges

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Example Question #1 : Electric Force Between Point Charges

Example Question #1 : Electric Force Between Point Charges

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