Three point charges are arranged in a horizontal line as...

Three point charges are arranged in a horizontal line as shown below. Find the electric force on Q? given the following: Q? = -5 µC, Q? = 1 µC, Q? = -5 µC, r? = 100 m, and r? = 150 m. Remember that a positive force points to the right and a negative force points to the left. Q? Q? Q? r? r? What is the net force on charge Q?? (in units of N) Submit Answer Tries 0/2 What is the net force on charge Q?? (in units of N) Submit Answer Tries 0/2 What is the net force on charge Q?? (in units of N) Submit Answer Tries 0/2 What is the sum of the forces on all three charges? (in units of N) Submit Answer Tries 0/2

Transcript

00:01 We have three point charges here as shown and the two distances, r sub 1 and r sub 2 are given.

00:06 So from that we know that the distance between charge 1 and charge 3 is 25 meters.

00:13 We are also given the magnitude and the sign of the three point charges.

00:18 We are to determine the net force acting on each charge and the total of these charges on the total force on these three charges.

00:30 We will be using the principle of superposition of forces and coulom's law in solving this problem.

00:37 So let's start with the total force on q1.

00:40 Let's identify the forces on q1.

00:43 Q2 is negative and we have q1 negative.

00:46 There will be a repulsive force.

00:48 So charge 2 will be repelling charge 1 to the left.

00:53 That's called this f sub 2 on 1.

00:55 And then charge 3 is positive here.

00:58 So there will be attractive force.

01:00 So q3 will exert a right toward force here.

01:05 Let's call this f sub 3 for the force of charge 3 on 1.

01:10 These are one dimensional forces.

01:13 So we'll just focus on the x axis.

01:18 Principle of superposition means we will just add these two forces algebraically.

01:24 So the total force on q1 would be positive f, 3 on 1, negative f 2 on 1.

01:35 Kulom's law will say that f sub 3 is, you have k magnitude of q sub 3 times the interacting charge q1, divided by the distance between them.

01:49 With respect to the symbols that we use here, distance between 1 and 3 is r sub 3 squared, minus force of 2 on 1.

02:01 Constant, charge 2, magnitude of charge 1.

02:06 Distance between 1 and 2 is r sub 1 squared.

02:13 Let's factor out k and q sub 1.

02:17 So electrical constant times the magnitude of q sub 1.

02:21 And then we will just have here q sub 3 over r3 squared minus q sub 2 over r1 squared.

02:30 Let's plug in the values now.

02:32 Concentrical constant let's use 9 to the 9th q1 magnitude is 2 mili in powers of 10 is 10 to negative 3 and then you have q sub 3 it's 3 mili column distance between 1 and 3 is 25 meters squared q2 is 5 mili distance between them is 10 squared therefore in newton's therefore the net force on q1 due to charges 1 and 2 is negative 814 newtons in three significant figures okay we'll do the same process in determining the net force on charge 2 so let's identify the forces on charge 2 repulsive force between 1 and 2 q1 will push this away this is is the force of 1 on 2.

03:38 And then another right toward force, attractive force, q3 will attract charge 2 towards it.

03:48 So we have two positive forces here, f sub 3 and f sub 1.

03:55 Okay...

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