An object of mass m=2.5 g and charge Q=+42 μC is attached to a string and placed in a uniform el

An object of mass m=2.5 g and charge Q=+42 μC is attached to...

Key Concepts

Uniform Electric Field

A uniform electric field is characterized by having the same magnitude and direction at every point in a given region. This consistency simplifies analysis since the force on a charge placed anywhere in the field will be the same, provided the charge remains constant. It is a central concept when analyzing problems involving charged objects in an electric field.

Force Decomposition

Force decomposition is the process of breaking a force into its horizontal and vertical components using trigonometric functions. This is particularly important in problems where forces are applied at an angle, as it allows for the independent analysis of the force components along each axis. Accurately resolving forces is key to applying the conditions of equilibrium properly.

Tension in a String

The tension in a string refers to the pulling force transmitted along it when it is subjected to forces at its ends. In equilibrium problems, the tension can be analyzed by resolving it into components that balance other forces acting on the object, such as gravitational and electrostatic forces. Understanding how tension counters these forces is essential in calculating its magnitude in such static conditions.

Electrostatic Force

This concept refers to the force experienced by a charge when it is placed in an electric field. The magnitude of the force is given by the product of the charge and the electric field strength (F = QE). This fundamental relationship allows one to determine the force acting on a charge due to an external field and is essential in solving problems related to charged particles in fields.

Static Equilibrium

Static equilibrium occurs when an object is at rest and the sum of all forces acting on it is zero. In such cases, each of the force components, typically resolved into perpendicular directions like horizontal and vertical, must individually balance. This concept is critical to ensure that an object remains stationary, allowing for the setup of equations that equate the net forces along each axis to zero.

Transcript

00:01 Question 91 states that an object of mass m equals 2 .5 grams and charge of positive 42 microculums is attached to a string and placed in a uniform electric field that is inclined at an angle of 30 degrees with the horizontal shown here.

00:17 So in my figure, the blue line is the string attached to the wall to the charge capital q.

00:24 The green lines represent the electric field, again with an angle of 30 degrees with the horizontal surface below it.

00:31 Object is in static equilibrium when the string is horizontal.

00:36 Find a, the magnitude of the electric field, and be the tension of the string.

00:43 So this question states that, at least relevant for part a, the sphere is in equilibrium when the angle, when the, i guess, yeah, the string is horizontal.

00:54 So that means in this scenario we're doing with a static problem.

00:57 So the net force acting on the sphere has to be zero.

01:02 So we need to look at what forces are acting on our object in order for this occur.

01:10 So i'm already to keep it in the right direction, which i'm going to call my x direction.

01:14 We need to look at the forces in this x direction and balance it with the y direction.

01:18 I guess it's just a y direction, right? because it's stable.

01:21 So we need to look at the y components of our force.

01:25 I guess you can look at x or y.

01:26 It doesn't really matter, but i'm going to look at y because, well, a couple of things, right? so the force is acting on it, of course, is gravity.

01:36 And the only thing that would be holding up is the force to the electric field.

01:41 Right? so force to the electric field has to count.

01:42 Counteracted force due to gravity, fg.

01:47 So that means, again, by our diagram, the electric force has to equate the electric, sorry, the gravitational force acting on the object.

01:56 So that gravitational force is, of course, just the weight of the object mass times gravity.

02:03 Whereas our electric force, we know that's just charge times the electric field.

02:09 However, the electric field is at an angle.

02:14 So if we want the y component of that, we look at our description here, you know that the y component of the electric field is given by the sign of the angle.

02:21 So that's times sine of 30, our sine theta output for now...

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