Physics 35 Coulomb's Law (3 of 8)

Summary

In this tutorial, the process of using Coulomb's law to calculate forces between charges is explained through a complex example. The video describes a setup with three charges: a positive 6 µC charge, a negative 4 µC charge, and another negative 8 µC charge. The focus is on calculating the force on the second charge due to the other two charges. The tutorial involves step-by-step calculations, including finding magnitudes, direction components, and the net force using vector addition. Additionally, it demonstrates how to apply Pythagoras' theorem and trigonometric functions to determine the resultant force's magnitude and direction.

Takeaways

• 😀 Coulomb's law helps in calculating the forces between charges based on their magnitudes and the distances between them.
• 😀 In this example, there are three charges: a 6 µC charge (q1) at the origin, a -4 µC charge (q2) two meters to the right, and a -8 µC charge (q3) two meters above q1.
• 😀 The goal is to determine the net force on q2 due to the other two charges.
• 😀 The forces on q2 from q1 and q3 are visualized as vectors, with q2 being attracted to q1 (since they are oppositely charged) and repelled by q3 (since they have the same charge).
• 😀 To calculate the net force, we find the magnitudes of the forces using Coulomb’s law for both interactions, F1,2 (between q1 and q2) and F2,3 (between q2 and q3).
• 😀 The magnitude of F1,2 is calculated as 0.054 N, and the magnitude of F2,3 is 0.036 N.
• 😀 To accurately sum the forces, the vector components of the forces need to be considered, including the X and Y components of F2,3.
• 😀 Using trigonometry, the X and Y components of the force between q2 and q3 are calculated based on the 45-degree angle formed by the line connecting the charges.
• 😀 The X component of the total force is found by adding the X components of both forces, resulting in -0.029 N, and the Y component is -0.025 N.
• 😀 The resultant total force is then calculated using the Pythagorean theorem, yielding a magnitude of 0.038 N at an angle of 41° below the negative X-axis.

Q & A

What is Coulomb's law and how is it applied in this problem?

Coulomb's law describes the force between two charges, given by the equation F = k * (q1 * q2) / r², where k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between them. In this problem, Coulomb's law is used to calculate the forces between the different charges placed in the system.

What is the setup of the problem involving three charges?

The problem involves three charges: a 6.0 microcoulomb charge (q1) placed at the origin, a -4.0 microcoulomb charge (q2) placed 2 meters to the right on the x-axis, and a -8.0 microcoulomb charge (q3) placed 2 meters above q1 on the y-axis.

What does the term 'force between charges' mean?

The force between charges refers to the electromagnetic force exerted on one charge due to the presence of another charge. This force can be either attractive or repulsive, depending on whether the charges are of opposite or like signs.

How do you determine the direction of the forces between the charges?

The direction of the force is determined by the types of charges involved. Opposite charges attract each other, so the force will point toward the other charge. Like charges repel each other, so the force will point away from the other charge.

What are the vector components of the forces, and why are they important?

The vector components of forces represent the forces in the x and y directions. Breaking the forces into components is necessary because the forces act in different directions, and to find the total force, we must sum the components separately in each direction.

Why is it necessary to use Coulomb's law to calculate the forces?

Coulomb's law is used to calculate the magnitude of the electrostatic force between charges, which depends on the magnitudes of the charges and the distance between them. This provides the necessary values to analyze the forces acting on the second charge in the system.

How do you find the magnitude of the total force after resolving the components?

To find the magnitude of the total force, we use the Pythagorean theorem, which combines the squared values of the x and y components of the forces and then takes the square root of the sum.

How do you calculate the angle of the total force relative to the x-axis?

The angle of the total force is calculated using the arctangent function, where the opposite side is the y-component of the total force and the adjacent side is the x-component. This gives the angle between the resultant force vector and the x-axis.

What is the significance of breaking down the forces into components?

Breaking down forces into components allows for easier vector addition since the forces act in different directions. By resolving the forces into x and y components, we can combine them algebraically and find the resultant force.

What is the final result for the total force on charge q2?

The total force on charge q2 is 0.038 N, with a direction of 41° below the negative x-axis. The x-component of the force is -0.029 N and the y-component is -0.025 N.