Quick Review: What do we already know about the electrostatic force? The electrostatic force is the force between stationary charges. Opposite charges attract. Same charges repel. We also know that this force is fairly strong and that it can act over a distance (but that the strength of this force decreases with the square of distance) Today, we will learn how to quantify the electrostatic force.
Calculating Electrostatic force: Coulomb’s Law Don’t forget: Force is a vector, so it has direction. You can reason out the direction of the force by remembering the opposites attract and like repel. What do the variables represent? k is “Coulomb’s law constant, and it has a value of q 1 and q 2 are the amount of charge (measured in C) of each object r is the distance between the objects (measured in m) Coulomb’s Law allows us to calculate the force between any two charged objects. Notice the similarities between the equations for electrostatic force and gravity: In both cases, the force increases with the size (mass or charge) of each object and force decreases as the distance between the object increases.
We do: Calculating Electrostatic Force 1)A charge of +2 mC and a charge of -3 mC are separated by 0.1m. What is the force between them? If the charges are each 0.001kg, what will be their acceleration? 2) Two charges are separated by a certain distance. If the distance between them is halved, how will the force change? F = 8.99 X 10 9 X 2X10 -6 X -3 X 10 -6 / (0.1) 2 F = -5N (attraction!) a = F / m = -5 N / 0.001 kg = 5000 m/s 2 The force will be quadrupled (four times bigger)
1. A woman accumulates a charge of 2.0 x 10 -5 C when sliding out of the seat of a car. A man has accumulated a charge – 8.0 x 10 -5 C while waiting in the wind. What is the force between them a)when she opens the door 6.0 m from him and b)when their separation is reduced by a factor of 0.5? You Do– Calculating Electrostatic Force 2. A positive charge is 0.5 m away from a negative charge. If the size of the positive charge is doubled and the distance is between them is also doubled, how will the force between the two charges change?
1. a) They exert equal forces on each other only in opposite direction b) r’ = 0.5 r (“-“ = attractive force) You Do– Calculating Electrostatic force 2. The force will be halved.
Electrostatic force when there are multiple charges Calculating the force between two charges is easy. What do you do if there are multiple charges? You can find the total force on any charge adding the forces from each other charge. Use Coulomb’s law to find the force from each individual charge, and make a free body diagram! Example: Charge Q is in between two other charges, arranged in a line. What is the total force on Q? q 1 = -5.0 Cq 2 = 4.5 C Q = -2.0 C d = 0.05 m d = 0.08 m Draw FBD for Q Q F1F1 F2F2 Use Coulomb’s Law to find F 1 and F 2 F 1 = 36 N F 2 = 13 N Since both forces are pointing in the same direction, they can just be added Total F = 49 N
Three point charges : q 1 = +8.00 mC; q 2 = -5.00 mC and q 3 = +5.00 mC. (a)Determine the net force (magnitude and direction) exerted on q 1 by the other two charges. (b)If q 1 had a mass of 1.50 g and it were free to move, what would be its acceleration? 1.30 m 23 0 q1q1q1q1 q2q2q2q2 q3q3q3q3 Calculating force from multiple charges in 2D: We Do Strategy: 1 st calculate forces from q2 and q3 2 nd separate each of those forces into x and y directions, 3 rd add the x components; add the y componets 4th use pythagorean theorem to find total force on q1
Three point charges : q 1 = +8.00 mC; q 2 = -5.00 mC and q 3 = +5.00 mC. (a)Determine the net force (magnitude and direction) exerted on q 1 by the other two charges. (b)If q 1 had a mass of 1.50 g and it were free to move, what would be its acceleration? 1.30 m 23 0 q1q1q1q1 q2q2q2q2 q3q3q3q3 Force diagram F2F2F2F2 F3F3F3F3 q1q1q1q1 electric force is very-very strong force, and resulting acceleration can be huge
Calculate force on +2 C charge due to other two charges HINT: –Calculate force from +7 C charge –Calculate force from –3.5 C charge –Add X and Y components from each –Use Pythagorean theorem to find total force total force Q=-3.5 C Q=+7.0 C Q=+2.0 C 6 m 4 m F7F7 5 m F3F3 Calculating force in more than one dimension: You Do
Calculate force on +2 C charge due to other two chargesCalculate force on +2 C charge due to other two charges –Calculate force from +7 C charge –Calculate force from –3.5 C charge –Add (VECTORS!) Q=-3.5 C Q=+7.0 C Q=+2.0 C 6 m 4 m F7F7 5 m F3F3 F x = F 7 cos + F 3 cos = F 7 (3/5) + F 3 (3/5) = 3 10 -3 N + 1.5 10 -3 N = 4.5 10 -3 N F y = F 7 sin + F 3 sin = F 7 (4/5) + F 3 (4/5) = 4 10 -3 N – 2.0 10 -3 N= 2.0 10 -3 N