VDU_Physics_3_012

## Solved University-Physics Problems

Physics 3:  Introduction to Electricity & Magnetism

## <<<  Electric Field between Charged Parallel Plates  >>>

Javier Montenegro Joo

## jmj@VirtualDynamics.Org

<<<  Electric Field between Charged Parallel Plates   >>>

(1) Two rectangular plates of sides “a” and “b” are placed so that an upwards vertical electric field “Eo” is established between both. Calculate the electric charge in each plate.

Solution.-

In order to find the connection between the electric field Eo between the plates and the charge on a plate consider a Gaussian surface as it is shown in the sketch:

(2) In the electric motor of an UFO that fell down in Cuzco, Peru, an electric condenser was found. The condenser consisted of two parallel plates of 20 cm x 30 cm, and between them an electric field of 50000 N/C was detected. Determine the electric charge in each plate.

Solution

[3] A sheet of a nonconducting material (may be a piece of paper) is loaded with a charge Q. Find the electric field at the surface of the sheet.

Solution.-

Since a sheet is rather thin the electric field generated by the charge is perceived at its both sides.  In order to find the electric field at the surface of the sheet, apply the Gauss theorem to a very  thin closed surface whose lateral sides are on both sides of the sheet. Under these conditions the electric field at each side of the sheet is normal, then:

[4] JMJ  The figure shows the charge densities on two very large sheets of nonconducting material which are placed vertical, parallel and, very close to each other. Determine the resultant electric fields at both sides of each sheet.

Solution.-

Bearing in mind that the electric field goes out of the positive charges and gets in the negative ones, use the sign of the charge density on each sheet to set the direction of the electric field produced by that sheet. Next use only the magnitude of each charge to compute the resultant electric field at the sides of the sheets, at points P1, P2 and P3:

Book : Algorithms of  Digital Image Processing and Pattern Recognition

by  Javier Montenegro Joo

[5]  The figure shows the charge densities on two very large sheets of nonconducting material which are placed vertical, parallel and, very close to each other. Determine the resultant electric fields at both sides of each sheet.

Solution.-

Bearing in mind that the electric field goes out of the positive charges and gets in the negative ones, use the sign of the charge density on each sheet to set the direction of the electric field produced by that sheet. Next use only the magnitude of each charge to compute the resultant electric field at the sides of the sheets, at points P1, P2 and P3:

[6] The figure shows the charge densities on three very large sheets of nonconducting material which are placed vertical, parallel and, very close to each other. Determine the resultant electric fields at both sides of each sheet.

Solution.-

Bearing in mind that the electric field goes out of the positive charges and gets in the negative ones, use the sign of the charge density on each sheet to set the direction of the electric field produced by that sheet. Next use only the magnitude of each charge to compute the resultant electric field at the sides of the sheets, at points P1, P2, P3 and P4: