A small 2.0 g plastic ball is suspended by a 20.0 cm string in a uniform electric field of 1.0 ×

A small 2.0 g plastic ball is suspended by a 20.0 cm string...

Key Concepts

Static Equilibrium

Static equilibrium refers to the condition in which an object remains at rest because the net force acting on it is zero. In such a situation, all individual forces, including gravitational, electric, and tension forces, balance each other out. Understanding static equilibrium is essential for analyzing systems where the object is suspended or fixed in place by various forces, as it allows for solving unknown quantities by setting the sum of forces in every direction equal to zero.

Free Body Diagram and Force Decomposition

A free body diagram is a graphical representation that illustrates all the forces acting on an object. By breaking these forces into their horizontal and vertical components, one can apply equilibrium conditions to each direction independently. This method of vector decomposition is crucial for problem-solving in mechanics, as it simplifies the analysis of forces acting at an angle, ensuring that each component is accurately accounted for in determining unknown variables such as charge or tension.

Uniform Electric Field

A uniform electric field is characterized by a constant magnitude and direction throughout the region it occupies. In such a field, any charged object experiences a force that is directly proportional to the magnitude of its charge, as given by F = qE. This concept is fundamental in understanding how the force on a charged object acts in a specific direction, which is determined by both the field’s orientation and the sign of the charge.

Electric Force on a Charge

The electric force on a charged object in an electric field is given by the product of the charge (q) and the electric field (E). This force is directional: a positive charge moves in the same direction as the electric field while a negative charge moves opposite to it. This principle allows one to determine the likely sign of a charge by observing the direction of the resulting force, making it key in both theoretical and practical electrostatics problems.

Transcript

00:01 Here's an example of a mass that's suspended by a string, and it is in an electric field that has a strength of 1 .0 times 10 to the 4 newtons per coulum, and it deflects.

00:18 And the reason why it deflects is because it is charged, and when a charged object is placed into a field, that that charged object is going to feel a force.

00:28 Now, the field is pointing to the right.

00:31 So that means that because these arrows are to the right, if you placed a positive test charge there, it would experience, excuse me, it would experience a force to the right.

00:43 So because this mass is deflecting to the right, we know that it's got to be positive because it's basically going in the direction of the field.

00:53 And so it's being repelled.

00:56 So the other thing that we can do is we can use these variables or values that are given to us to find what is the net charge on that object.

01:06 So the way that we always start these kinds of problems is you want to start by drawing a force, a free body diagram or a force diagram on this mass.

01:14 So i'm basically just doing this here.

01:18 And i know that it has a mass, so it has to have a force of gravity on it, a weight.

01:22 And there's a tension pulling it along the string and there's a repelling force that's from the electric field and that's got to be equal to the x component of this tension in fact i don't normally like drawing it a solid line i like making it a dotted line so you can see that these aren't new forces they're just tension forces that are broken up we know this angle here is 15 so what we can do is is since we know that this has to be equal to that, we can solve for what that fe is going to be by using fg, because also f -t -y has to be equal to f -g.

02:06 Now, how do i know that that's true? well, it's in equilibrium.

02:10 And equilibrium means that all the forces have to add up, oops, that's an f.

02:16 All the forces have to add up to zero.

02:18 So if we have only two forces in the y direction, this one and this one, one, then they have to cancel.

02:26 And if we have only two in the x direction, this one, and this one, then they also have to cancel.

02:30 So what we're going to do is we're going to solve for fg.

02:34 It's mass times g, which is g is 9 .8.

02:38 Mass is 2, but that's 2 grams.

02:41 So that means it has to be 0 .02 kilograms.

02:47 And g is 9 .8.

02:49 So let's calculate that...