Three point charges lie along a straight line as shown in Figure P 23.8, where q1=6.00 μC, q2=1.

Three point charges lie along a straight line as shown in...

Key Concepts

Sign Conventions in Electrostatics

Proper consideration of the sign of electric charges is crucial as it influences both the magnitude and direction of the forces involved. The sign conventions help identify whether forces are attractive or repulsive, which is essential when setting up the vector sum of forces in a system of charges.

Coulomb's Law

Coulomb's Law provides the quantitative expression for the force between two point charges. It states that the magnitude of the force is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them. This law is fundamental in calculating electrostatic forces in any system of charges.

Superposition Principle

The Superposition Principle asserts that the net force acting on any charge is the vector sum of the individual forces that each of the other charges exerts on it. This principle allows for the analysis of complex charge configurations by breaking them down into pairwise interactions and then summing up the contributions.

Electric Charge Interactions

Electric charge interactions are governed by the fact that like charges repel each other while opposite charges attract. This fundamental behavior is essential for understanding how different charges will interact and determine the overall force direction in systems where multiple charges are present.

Vector Addition

In the context of electrostatics, forces are vector quantities, meaning they have both magnitude and direction. Vector addition is used to combine these forces accurately, taking into account their directions, to determine the net force acting on any particular charge.

Transcript

00:01 Okay, so the electric force on q1 can be expressed like this, which is kq1, q2 over d1 square plus kq1, q3 over d1 plus d2 square.

00:11 It's because q1 will receive two forces.

00:15 One is the attractive force from the q3 because q3 is negative charge and q1 is positive charge.

00:21 And another force is the repulsive force from q2 because q2 and q1 are both positive.

00:26 Okay? so if you do some arrangement, you eventually have k21 times.

00:30 Q2 over d1 square plus q3 over d1 plus d2 square.

00:35 We know the k, which is the coolon constant, is equal to 9 -10 -10 -power -9 -n -0 -0 -0 -tenth -medial square for cool -on square.

00:41 And q1 is given as 6 micro -coolon, which is 6 times 10 -2 -power -9 -6 -cologne.

00:47 And q2 is given as 1 .50 -mile -cholon, which is 1 .50 -t times 10 -2 -p0 -9 -6 -cologne.

00:54 And q3 is the negative charge, which is negative -cholon, which is negative -2 times 10 -2 -0 -0 -0 -0 -0 -6.

01:00 And the distance between q1 and q2 is d1, which is 3 .3 centimeter, and if we convert to meter, is 3 times 10 to power negative 2 meter.

01:11 And d2, which is the distance between q2 and q3, is 2 .00 centimeter, which is 2 times 10 to negative 2 meter.

01:18 So the distance between q1 and q3 is 3 centimeter plus 2 centimeter, which is 5 centimeter.

01:25 And if we convert it to meter is 5 times 10 to 0 % negative 2 meter.

01:30 So now, let's start our calculation.

01:33 So the force on q1 is equal to 9 .0 times 10 to the power of 9 newtons, times mdun square per cullon square, and then times charge, which is 6 .00, times 10 to the power of negative 6, cologne.

01:55 And then times charge q2, which is 1 .50 times 10 to the power of negative 6 cullon over 3 .00 times 10 to the power of negative 2 meter and then square plus q3 which is negative 2 .0 times 10 to the power of negative 6 colon and then over 5 .00 okay because 3 centimeter plus 2 centimeter is 5 centimeter which is 5 .0 times 10 to the power of negative 2 meter and then squared and this will give us the electric force on q1 is about 46 .8 newtoms.

02:50 Okay, so since it's a positive force, that means the direction of the electric force on q1 is to the left, okay? because if it's positive, that means the repulsive force from the positive charge is greater than the attractive force from negative charge.

03:10 And we know the repulsive force from q2 has a direction to the left, because you're trying to repose q1 to the left.

03:18 So the direction for the force on q1 is left.

03:22 And let's take look at the electric force on q2.

03:27 Well, this is the equation of the electric force on q2, which is equal to k, q1, q2 over d1 square, plus k q2, q2, over d2 square...

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