- #1

tellmesomething

- 327

- 38

- Homework Statement
- Q1) Why did he make the cylinder's height infinite and the thick slab's plane infinite...?

Q2)I dont understand what he meant by them having dimensional symmetry...symmetry of what? electric fields? and how did he get that it will 1, 2 or 3..Can someone explain this...?

Context below..

- Relevant Equations
- None

I derived an expression for the electric field due to solid uniformly charged non conducting spherical volume to be

$$ \frac{ Qz} {4π\epsilon R^3 } $$ where z is the distance of the point from the center and it is less than the radius R I.e the point lies inside the sphere...

This in terms of volume charge density can also be written as $$ \frac{\rho z } { 3 \epsilon } $$

A teacher whose video lessons i follow then gave us the expressions for the field at a point inside a cylinder whose height is infinite but cross sectional area is finite

$$ \frac{ \rho z } {2 \epsilon} $$

Where z is the distance from the line of symmetry ..

and the field at a point inside a thick slab whose length and thickness is infinite but breadth is finite...

$$ \frac{ \rho z } { \epsilon} $$

Where z is the distance from a plane of symmetry..

He then went on to explain that the sphere has 3d symmetry the cylinder has 2d symmetry and the slabs have 1d symmetry..and thats a way to remember these results...

Q1) Why did he make the cylinder's height infinite and the thick slab's plane infinite...?

Q2)I dont understand what he meant by them having dimensional symmetry...symmetry of what? electric fields? and how did he get that it will 1, 2 or 3..Can someone explain this...?

$$ \frac{ Qz} {4π\epsilon R^3 } $$ where z is the distance of the point from the center and it is less than the radius R I.e the point lies inside the sphere...

This in terms of volume charge density can also be written as $$ \frac{\rho z } { 3 \epsilon } $$

A teacher whose video lessons i follow then gave us the expressions for the field at a point inside a cylinder whose height is infinite but cross sectional area is finite

$$ \frac{ \rho z } {2 \epsilon} $$

Where z is the distance from the line of symmetry ..

and the field at a point inside a thick slab whose length and thickness is infinite but breadth is finite...

$$ \frac{ \rho z } { \epsilon} $$

Where z is the distance from a plane of symmetry..

He then went on to explain that the sphere has 3d symmetry the cylinder has 2d symmetry and the slabs have 1d symmetry..and thats a way to remember these results...

Q1) Why did he make the cylinder's height infinite and the thick slab's plane infinite...?

Q2)I dont understand what he meant by them having dimensional symmetry...symmetry of what? electric fields? and how did he get that it will 1, 2 or 3..Can someone explain this...?

Last edited: