Two square, oppositely charged conducting plates measure 20 cm on each side. The plates are clo

Two square, oppositely charged conducting plates measure 20...

Two square, oppositely charged conducting plates measure $20 \mathrm{~cm}$ on each side. The plates are close together and parallel to each other. They each have a total charge of $+4.0 \mathrm{nC}$ and $-4.0 \mathrm{nC},$ respectively. (a) What is the electric field between the plates? (b) What force is exerted on an electron located between the plates? (c) What would be the electron's acceleration if it were released from rest?

Two square, oppositely charged conducting plates measure $20 \mathrm{~cm}$ on each side. The plates are close together and parallel to each other. They each have a total charge of $+4.0 \mathrm{nC}$ and $-4.0 \mathrm{nC},$ respectively.
(a) What is the electric field between the plates? (b) What force is exerted on an electron located between the plates? (c) What would be the electron's acceleration if it were released from rest?

Key Concepts

Newton's Second Law for Particle Acceleration

Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, as given by F = ma. This concept is used to determine the acceleration of a charged particle, like an electron, when the force exerted by the electric field is known.

Force on a Charge in an Electric Field

When a charged particle is placed within an electric field, it experiences a force proportional to both the charge and the magnitude of the electric field, in accordance with the equation F = qE. This principle is essential for analyzing the motion of charged particles, such as electrons, when subjected to electric fields.

Surface Charge Density

Surface charge density is defined as the amount of charge per unit area on a surface. It plays a crucial role in determining the electric field created by each plate. For uniformly charged plates, the surface charge density can be calculated by dividing the total charge by the area of the plate, providing the basis for finding the electric field between the plates.

Uniform Electric Field

In the region between two oppositely charged, parallel plates that are close together, the electric field is nearly uniform. This means that the strength and direction of the electric field remain nearly constant throughout the space between the plates, simplifying calculations of field strength and forces on charges within the region.

Transcript

00:01 2 square plates of side d equals to 20 cm, that is 0 .20 meter, and charge on the each plate is equivalent magnitude and opposite nature.

00:12 So q is equal to plus 4 .0 nanoculum, that is plus 4 .0 multiplied by 10 to the power minus 9 column.

00:21 And this is so plus minus q, so we can write here plus minus q.

00:26 Okay.

00:26 So for the part a of the question in which we have to calculate the electric field between the plates.

00:31 So electric field between the plates of oppositely charged is equal to q by a epsilon not, where q is the charge of one plate, so it is small q here and area will be d square multiplied by epsilon.

00:45 Epsilon not is the permittivity of the medium.

00:47 And so substituting values we get q is equal to 4 .0 multiplied by 10 to the power minus 9 column divided by d is equal to 0 .20 meter, so whole square and epsilon not is a 8 .85 multiplied by 10 to the power minus 12.

01:03 Okay, so from here after solving, we get electric field between the plates e equals to 1 .1 multiplied by 10 to the power 4 newton per column.

01:13 Okay, so this is the answer for the part a of the problem.

01:17 Now, moving to the part b in which we have to calculate the force exerted on the electron located between the plates.

01:24 So force on and charge particle is given by f equals to qe and qe here, here, is electron.

01:31 So electron has charged small e...

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