{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture 06 - Electric field lines

# Lecture 06 - Electric field lines - EXAMPLE Ring Below is a...

This preview shows pages 1–3. Sign up to view the full content.

1 Lecture 6 Electric fields in dielectrics and conductors. Electric field lines. EXAMPLE: Ring Below is a ring of radius R with uniform linear charge distribution λ . Find the electric field along the z -axis. x P y z x z d θ d q = λ Rd θ r = + 2 2 R z P y 2 dq dE k r = G 2 2 Rd k R z λ θ = + cos z dE dE ϕ = G 2 2 2 2 Rd z k R z R z λ θ = + + x P z Cylindrical symmetry: only E z matters φ zRd λ θ y ( ) 3/2 2 2 k R z = + ( ) 2 , net 3/2 0 2 2 z zR E k d R z π λ θ = + ( ) 3/2 2 2 2 zR k R z πλ = +

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 From the ring to the charged disk… Disk of radius R with uniform surface charge density σ can be thought of as made of rings of radii r = 0 to r = R and linear charge density σ dr. ( ) πσ = disk 3/2 2 R R zr E k dr ( ) πσ = − 1/2 1 2 R k z + 0 2 2 r z + 2 2 0 r z ( ) πσ = − + 1/2 2 2 1 1 2 k z z r z ( ) πσ = + 1/2 2 2 2 1 z k R z ( ) σ ε = + 1/2 2 2 0 1 2 z R z … and to the infinite plane Take the limit R ( ) σ σ
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

Lecture 06 - Electric field lines - EXAMPLE Ring Below is a...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online