Coulomb's Law

Question 1

what is the equation for the force between two charged particles Q1 and Q2 which are separated by a distance r

Answer 1

F(e) = Q1 Q2 / 4 pi e(0) r^2

Question 2

what is the name of this equation

Answer 2

coulombs law

Question 3

what type of force is F

Answer 3

an electric force, F(e)

Question 4

what is the definition of the constant e(0)

Answer 4

• the permittivity of free-space

- the 0 refers to the permittivity of air

Question 5

what is the value of e(0)

Answer 5

8.85x10-12

Question 6

given that 1 / 4 pi e(0) = k, how would we rewrite coulombs law for simplicity’s sake

Answer 6

F = k Q1 Q2 / r^2`

Question 7

therefore what is the value of k

Answer 7

k = 8.99x10^9

Question 8

given F = EQ, what would electric (radial) field strength equate to using coulombs law (already in the other deck)

Answer 8

• E = Q / 4 pi e(0) r^2

- E = k Q / r^2

Question 9

what type of fields does coulombs law only apply to

Answer 9

radial fields

Question 10

what is r in the equation specifically

Answer 10

the distance between the centres of both charged spheres

Question 11

what would a negative and positive force tell you about the interactions between the charges

Answer 11

• a negative force tells you the spheres attract

- a positive force tells you the spheres repel

Question 12

why does a negative force tell you the points of charge are attracting (and vice versa with a positive force)

Answer 12

• a negative force tells you that one charge is +ve and the other is -ve
• as they are multiplied in F = k Q1 Q2 / r^2, that you giv you a -ve force
• with 2 +ve or -ve charges that repel, F would be positive

Question 13

what law does coulombs law follow and why

Answer 13

• the inverse square law
• because F is inversely proportional to 1 / r^2
• when r doubles, the force is cut into 1/4

Question 14

why is it said that things that seem to be touching arent technically touching

Answer 14

• the outer layer of an atom consists of electrons (shells)
• this means that when one object comes close to another, these electrons repel each other
• this repulsion causes the two objects to never actually touch
• but it would look / feel that way because of the repulsive force between them

Question 15

two balls (eg balloons) are tied to opposite ends of a piece of string. the string is hung from the middle so the balls are hanging, aligned. given that the balls are charged and have the same charge, causing them to repel, what would free-body diagram of each ball look like

Answer 15

• its weight (mg) would be acting vertically downwards
• the electric force exerted on it (F(e)) would be acting horizontally away (pointing away from both balls)
• tension would be acting upwards along the piece of string

Question 16

taking the right angled triangle formed from a ball being repelled, the angle between the string and the middle of the bigger triangle (the normal to r, the distance between the two balls) is theta (0), the length of that normal is L and the distance between the centre of the ball and the normal is d (1/2 r). knowing all this, what equation would you derive to calculate tension, given that you know the mass of the ball

Answer 16

• w = mg
• the vertical component of tension is equal to weight
• so cos0 = a / h is cos0 = mg / T
• T = mg / cos0

Question 17

given that you know tension, what equation would you derive to calculate the electric force

Answer 17

• the horizontal component of tension is equal to electric force
• sin0 = o / h so sin0 = F / T
• F = T sin0

Question 18

if you werent given the angle, but you knew the total length of the string and d, how would you calculate 0

Answer 18

• the hypotenuse is half the length of the total string
• as you know h and o
• sin0 = o / h, then inverse

Question 19

given that mg = T cos0 and F = T sin0, what does tan0 equal

Answer 19

• sin0 / cos0 = F / mg

- tan 0 = F / mg

Question 20

what is another thing you could equate tan0 to

Answer 20

• tan0 = d / L

- its an approximation that works better with long pieces of string

Question 21

using this, show that Q1 Q2 / 4 pi e(0) r^2 = mgd / L

Answer 21

• d / L = F / mg
• F(coulomb) = mgd / L
• as F(coulomb) = Q1 Q2 / 4 pi e(0) r^2
• Q1 Q2 / 4 pi e(0) r^2 = mgd / L

Question 22

for a fixed amount of charges, what kind of graph would varying r and measuring d allow you to plot

Answer 22

• a graph of 1 / r^2 against d

- the line should be straight

Question 23

because it is difficult to control the amount of charge placed on the spheres, what could you practically do in order to confirm that F is proportional to the product of the two charges

Answer 23

• charge both the spheres up
• touching one of them with a third sphere to remove half the charge on that one
• repeat this many times and measure d each time