Concept explainers
A small portion near the center of a large thin
Write an expression for the charge density on each side of the conducting plate.
The expression for charge density on each side of the conducting plate.
Explanation of Solution
Introduction:
The charge density is the ratio the charge distributed over a surface area. The expression for the charge density is given by,
The distribution of the charge on the plate is shown below,
Figure 1
Now, because plate in uniform and charge on both the sides is same. So, the charge density on both the sides of the plate if the area of the sides is
Conclusion:
Therefore, the expression for the charge density on each side of the plate is
Want to see more full solutions like this?
Chapter 5 Solutions
Tutorials in Introductory Physics
Additional Science Textbook Solutions
University Physics (14th Edition)
An Introduction to Thermal Physics
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
The Cosmic Perspective (8th Edition)
Essential University Physics: Volume 1 (3rd Edition)
College Physics (10th Edition)
- Positive electric charge is uniformly distributed along the y-axis with a linear charge density l. Consider the case where charge is distributed only between points y = +a and y = -a. For points between the +x-axis, graph the x-component of the electric field as a function of x, Ex (x), for values x = a/2 and x = 4a. Consider instead the case where charge is distributed along the entire y-axis with the same charge density l. Using the same graph as in part (a), plot the x-component of the electric field, Ex (x), as function of x for values of x between x = a/2 and x = 4a.arrow_forwardA thin rod is bent into a circular arc that subtends an angle 2θ of a circle centered at P. A total charge, Q, is distributed uniformly over the full rod. Let the positive x direction be towards the right of the page, and the positive y direction is towards the top of the page. In Cartesian unit-vector format, what is the electric field at P?arrow_forwardA non-uniform thin rod is bent into an arc of radius R. The linear charge density λ of the roddepends on θ and is given byλ =λ0/cos θwhere λ0 is a positive constant. The arc extends from θ =π/4 to θ =3π/4as shown a)Sketch the direction of the resultant electric field at the origin.b) Calculate the magnitude of the electric field E->.arrow_forward
- A hollow sphere made from a non-conducting material is shown below in cross-section. The inner radius is R1, and the outer radius is R2. The material is charged uniformly -ρ.(a) Using Gauss’ Law, find an expression in terms R1, R2, and ρ of the magnitude(measured in N/C) and the direction (away from or towards the center) of the electricfield at a distance r from the center of the sphere, for values R1 < r < R2? (Do all thiswork symbolically - don't use the values of part (b) for this part.) (b) The inner radius is R1 = 1.00 cm, and the outer radius is R2 = 4.00 cm. Thematerial is charged uniformly ρ = -1.70 nC/m3. If the electric potential is 0V infinitely faraway, what is the electric potential at the outer surface (r = R2) of the sphere? Please show full work Thank you!arrow_forwardThree chargesbare arranged on a rectangle as shown below. What is the net electric field at P2? Calculate the magnitude and the directionarrow_forwardThe figure shown above displays a cross section of a three-dimensional closed surface with a flat top and bottom surface above and below the plane of the page. If there is no flux through the top or bottom surface, the electric field is everywhere parallel to the page and is uniform over each face of the surface, which of the following is true? There is no net charge enclosed. There is a negative net charge enclosed. There is a positive net charge enclosed.arrow_forward
- In the configuration shown in the picture below, what is the total predicted angle for electric field at point a?arrow_forwardA charge q is placed in the cavity of a conductor as shown below. Will a charge outside the conductor experience an electric field due to the presence of q? The conductor in the preceding figure has an excess charge of -5.0 uC. If a 2.0 uC point charge is placed in the cavity, what is the net charge on the surface of the cavity and on the outer surface of the conductor?arrow_forwardThe charge per unit length on the thin rod shownbelow is λ . What is the electric field at the point P? (Hint:Solve this problem by first considering the electric fieldd E→ at P due to a small segment dx of the rod, whichcontains charge dq = λdx . Then find the net field byintegrating d E→ over the length of the rod.)arrow_forward
- Consider two long, thin, concentric cylindrical shells. The smaller shell has a radius ‘a’ and carries a uniform surface charge density +σ. The larger shell has a radius ‘b’ and carries a surface charge density −2σ. Your answers for this problem should only depend on the variables r, σ, and ε0. A section of the two cylinders is shown to the right. (a) Find an expression for the electric field as a function of r (distance from the center of the cylinders), for r < a. (b) Find an expression for the electric field as a function of r, for a < r < b. (c) Find an expression for the electric field as a function of r, for r > b.arrow_forwardConsider a quarter-circular, very thin, curved rod with a uniform linear charge density, λ, and aradius, r. Derive an equation for the magnitude of the electric field at the point, P, at the centercurvature of the rod, as shown in the figure below. Write the final answer in terms of λ and r, and simplify your answer as much as possible.arrow_forwardA very long line of charge with a linear charge density, , is parallel to another very long line of charge with a linear charge density, 2. Both lines are parallel to the y-axis, and are the same distance r from the y-axis, where the first wire is to the left of the origin and the second is to the right. Use Gausss law and the principle of superposition to find an expression for the magnitude of the electric field at the origin.arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill