
Two large conducting plates are placed parallel to each other with a separation of between them. An electron starting from rest near one of the plates reaches the other plate in microseconds. Find the surface charge density on the inner surface.
Answer
153.6k+ views
Hint: The motion of the electron is caused by the electric field between the plates and the force pulling the electron is electrostatic force between the two plates. Calculate the value of the acceleration and apply in the formula for the electrostatic force of attraction to find the value of the surface charge density.
Complete step by step answer:
It is given that an electron is travelling from one plate to the other which are separated by a distance of .
Distance between the two plates,
Time taken by the electron to travel from one plate to other,
The field between the plates and the electrostatic force causing the electron to travel between the two plates.
Here we are asked to find the value of the surface charge density on the inner surface,
It is known that, the electric field,
Where, is the surface charge density
is the permittivity of the vacuum=
We know electrostatic force,
Where, is the charge of electron =
Applying the value of the electric field, we get,
...........................equation (1)
But we know the force given by mass is multiplied by the acceleration.
That is, ............................equation (2)
Where, is the mass of the electron =
is the acceleration
Acceleration is given by,
So equation 2 will become, .................equation (3)
That is, from equations 1 and 3 we get,
Applying all the known values we get,
That is the surface charge density on the inner surface, .
Note: The electrostatic force or Coulomb force is capable of acting through space, producing an effect even when there is no physical contact between the particles involved. Since there is no physical contact required for this interaction, it is assumed that there exists an electric field around a charged particle. When another charged particle enters this electric field, forces of an electrical nature are formed.
Complete step by step answer:
It is given that an electron is travelling from one plate to the other which are separated by a distance of
Distance between the two plates,
Time taken by the electron to travel from one plate to other,
The field between the plates and the electrostatic force causing the electron to travel between the two plates.
Here we are asked to find the value of the surface charge density on the inner surface,
It is known that, the electric field,
Where,
We know electrostatic force,
Where,
Applying the value of the electric field, we get,
But we know the force given by mass is multiplied by the acceleration.
That is,
Where,
Acceleration is given by,
So equation 2 will become,
That is, from equations 1 and 3 we get,
Applying all the known values we get,
That is the surface charge density on the inner surface,
Note: The electrostatic force or Coulomb force is capable of acting through space, producing an effect even when there is no physical contact between the particles involved. Since there is no physical contact required for this interaction, it is assumed that there exists an electric field around a charged particle. When another charged particle enters this electric field, forces of an electrical nature are formed.
Recently Updated Pages
JEE Main 2022 (June 29th Shift 2) Maths Question Paper with Answer Key

JEE Main 2023 (January 25th Shift 1) Maths Question Paper with Answer Key

JEE Main 2022 (July 29th Shift 1) Maths Question Paper with Answer Key

JEE Main 2022 (July 26th Shift 2) Chemistry Question Paper with Answer Key

JEE Main 2022 (June 26th Shift 2) Maths Question Paper with Answer Key

JEE Main 2022 (June 29th Shift 1) Physics Question Paper with Answer Key

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Degree of Dissociation and Its Formula With Solved Example for JEE

Displacement-Time Graph and Velocity-Time Graph for JEE

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Electrical Field of Charged Spherical Shell - JEE

Ideal and Non-Ideal Solutions Raoult's Law - JEE
