Electric Charge and Electric Field Problem

[lawk]

Homework Statement

Two small spheres, each of mass 8.00 g , are suspended by light strings 15.0 cm in length (see figure). A uniform electric field is applied in the x direction. The spheres have charges equal to -6*10^-8 and 6*10^-8 Determine the electric field that enables the spheres to be in equilibrium at an angle of 11 degree.

Homework Equations

ke = 8.99*10^9
gravity= 9.8 m/s^2

ke(q1*q2)/r^2 ?

The Attempt at a Solution

I don't know how to approach the problem.
I don't know how gravity is affecting the problem.
Can someone guide me through the problem?
What should I do in order to get the answer?

 

[Defennder]

If you examine the diagram, you'll see that there are 3 forces acting on the system. Two of them, electrostatic attraction between the positive and negative charges and gravity cause the spheres to move closer together, and downwards respectively. The 3rd force, that due to the applied E-field, repels the positive charge and attracts the negative one. Those 3 forces in conjunction create a static equilibrium. Your job is to find the magnitude of the E-field applied.

Note that you must take into account the E-field due to either the positive or negative charge (unless it's small enough to be negligible).

 

[Tina20]

Can someone please help with this question :) I am confused as to what to do as well :(

Tina

 

[Redbelly98]

Have you drawn free-body diagrams showing the forces on each sphere? You'll need to show an attempt at solving the problem before we can help you out more.

 

[rwisz]

I can provide guidance on how to approach this problem. First, it is important to understand the concept of electric charge and electric fields. Electric charge is a fundamental property of matter that can be positive or negative, and it creates an electric field around it. The strength of the electric field is dependent on the magnitude and distance of the charges. In this problem, we have two small spheres with opposite charges suspended in an electric field.

To solve this problem, we need to use the principle of equilibrium. This means that the forces acting on the spheres must balance out, resulting in no net force and therefore no movement. In this case, we have two forces acting on each sphere - the electric force and the force of gravity.

To start, we can calculate the electric force between the two spheres using Coulomb's law, which states that the electric force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This can be expressed as:

Fe = ke * (q1 * q2) / r^2

Where ke is the Coulomb's constant (8.99*10^9), q1 and q2 are the charges of the spheres, and r is the distance between them.

Next, we need to consider the force of gravity acting on each sphere. This can be calculated using the formula:

Fg = m * g

Where m is the mass of the sphere and g is the acceleration due to gravity (9.8 m/s^2).

Now, since we want the spheres to be in equilibrium, the sum of the forces in the x-direction (horizontal) and y-direction (vertical) must be equal to zero. This can be expressed as:

∑Fx = Fe * cosθ = Fg

∑Fy = Fe * sinθ = T (tension in the string)

Where θ is the angle at which the spheres are suspended, and T is the tension in the string.

Since we know the mass of the spheres and the angle at which they are suspended, we can solve for the tension in the string. Once we have the tension, we can use it to solve for the electric field by equating the forces in the x-direction:

Fe * cosθ = T

Now, we can solve for the electric field using the equation:

E = T / (q * d)

Where q is the charge of the spheres and d is the separation