Question

In: Physics

Electrostatic Force and Equilibrium Consider a rhombus with side of length L. The rhombus has two...

Electrostatic Force and Equilibrium

Consider a rhombus with side of length L. The rhombus has two pair
of equal interior angles. Label one of these pair θ and the other φ. Four
identical, positive point charges, q are placed on the vertices of the rhombus.
Draw the configuration.

a) Obtain a symbolic expression for the electric field at one of the vertices
(your choice) and then at an adjacent vertex (Do you now know the electric
field at all of the vertices? Why/why not?). Does it matter that there is a
charge at the vertex? Comment on the direction of the electric field at your
two vertices. Does this make sense? Why?

b) We now allow the angles to vary, subject to the constraint that the figure
must remain a rhombus. Label one of the vertices P. What θ value and φ
value, (in degrees), minimizes the electric field at P . Hint: You should only
have to do one minimization, as there is a constraint between θ and φ.

c) Plot the magnitude of the electric field at P as a function of the angle
opposite P ( This will be θ or φ depending on how you labeled your figure).

Please show your work and explanation. Thanks for your help.

Solutions

Expert Solution

genius_generous answered 1 year ago
Next > < Previous

Related Solutions

The side of a rhombus forms two angles with its diagonals such that their difference is...
The side of a rhombus forms two angles with its diagonals such that their difference is equal to 30 degrees. What are the angles of the rhombus?
The drawing shows a square, each side of which has a length of L = 0.250...
The drawing shows a square, each side of which has a length of L = 0.250 m. Two different positive charges q1 and q2 are fixed at the corners of the square. Find the electric potential energy of a third charge q3 = -3.00 x 10-9 C placed at corner A and then at corner B.
The perimeter of a rhombus is 560 meters and one of its diagonals has a length of 76 meters. Find the area of the rhombus.
The perimeter of a rhombus is 560 meters and one of its diagonals has a length of 76 meters. Find the area of the rhombus. Part A: Determine the length of the other diagonal. Part B: The area is _______  square meters.
Challenge #1: How is electrostatic force (Felect) related to the magnitude of charge on the two...
Challenge #1: How is electrostatic force (Felect) related to the magnitude of charge on the two objects? Keeping the separation distance for all trials the SAME, change the magnitude of the charges and record the force. Charge on 1 (q1) Charge on 2 (q2) Force (Felect) 5 C 200 C 1 N Is the relationship between MAGNITUDE of the electric charge and FORCE different today than it was yesterday? What type of relationship is this? Positive/Negative Linear/Non-linear The arrows in...
Three charges of +Q are at the three corners of a square of side length L....
Three charges of +Q are at the three corners of a square of side length L. The last corner is occupied by a charge of -Q. Find the electric field at the center of the square.
A cube with side length L, and density ρC sits at rest on a bathroom scale...
A cube with side length L, and density ρC sits at rest on a bathroom scale at the bottom of a large tank. The tank is partially filled with a fluid having density ρf, leaving the cube partially submerged. A side profile view of the cube shows the cube face a distance d outside of the fluid, and a distance L-d submerged under the fluid. Determine the distance dwhen ρf= 2000 kg/m3, ρC= 4000 kg/m3and L = .50 m. Write...
Consider a two-dimensional electron gas in a square box of side L, with periodic boundary conditions....
Consider a two-dimensional electron gas in a square box of side L, with periodic boundary conditions. a) Derive the density of states per unit energy, D(ε). b) Find the Fermi wavevector, kF, and the Fermi energy, εF, in terms of the number of electrons N and the area of the box, A=L2 . c) Calculate the density of states at the Fermi energy, D(εF), expressed in terms of N and A. Calculate the heat capacity, CV.
Consider a two-dimensional electron gas in a square box of side L, with periodic boundary conditions....
Consider a two-dimensional electron gas in a square box of side L, with periodic boundary conditions. a) Derive the density of states per unit energy, D(ε). b) Find the Fermi wavevector, kF, and the Fermi energy, εF, in terms of the number of electrons N and the area of the box, A=L2 . c) Calculate the density of states at the Fermi energy, D(εF), expressed in terms of N and A. Calculate the heat capacity, CV.
Consider a rhombus that is not square (i.e., the four sides all have the same length, but the angles between sides is not 90°).
Consider a rhombus that is not square (i.e., the four sides all have the same length, but the angles between sides is not 90°). Describe all the symmetries of the rhombus. Write down the Cayley table for the group of symmetries,
Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of -0.8803...
Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of -0.8803 N when separated by 50 cm, center-to-center. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0921 N. What were the initial charges on the spheres? Since one is negative and you cannot tell which is positive or negative, there are two solutions. Take the absolute value of...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT