Proportionalities R A aA a  ? 1. R- r 2. R+ r 3. R 2 / r 2 4. R 2 / r 5. R/ r 6. r /R a A r.

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Presentation transcript:

Proportionalities R A aA a  ? 1. R- r 2. R+ r 3. R 2 / r 2 4. R 2 / r 5. R/ r 6. r /R a A r

Proportionalities R A aA a  ? 1.  R/ r 2. R/  r 3. R 2 / r 2 4.  R 2 / r 5. R/ r 6. r 2 /R 2 a r A

The same proportionalities work for arc-lengths R S R s r  r S s area at S R 2 area at s r 2 

The electric field at the very CENTER of this spherical conductor E = ? 1. points out 2. points in 3. points up 4. points left 5. points right 6.points down 7.is zero

What is the electric field at the very CENTER of this spherical conductor? E = 0!!

The electric field at this off-CENTER point within the spherical conductor E = ? 1. points out 2. points in 3. points up 4. points left 5. points right 6.points down 7.is zero

Q=? q=?q=? Q/q=? R r

Electrical Shielding In the presence of any nearby electric field the charge carriers within a conductor distribute themselves to effectively cancel the field in their own interior! - + NO FIELD! The interior is “shielded” from external magnetic fields

Gauss’ Law FLUX = E  A FLUX = “flow” number of lines entering or leaving a region (volume)

If more lines enter than leave denotes a concentration of negative charge within If more lines exit than enter denotes a concentration of positive charge within

A cube with edge, L, and surface area A on each face, is immersed in a uniform electric field E as shown. The flux through its bottom surface is 1.+ EA  EA 3.+ EL  EL 5. 0

A cube with edge, L, and surface area A on each face, is immersed in a uniform electric field E as shown. The flux through its top surface is 1.+ EA  EA 3.+ EL  EL 5. 0

A cube with edge, L, and surface area A on each face, is immersed in a uniform electric field E as shown. The flux through its front-facing surface is 1.+ EA  EA 3.+ EL  EL 5. 0

A cube with edge, L, and surface area A on each face, is immersed in a uniform electric field E as shown. The total flux through this cube is 1.+ 2EA  2EA 3.+ 6EL  4EL 5. 0

Flux = E  A Flux = 0 Flux = ?

Gaussian Surfaces

Heated filamentPositively charged can If the effective field is E =800,000 N/C over a gap length of 2.5 cm, what is the electron’s final velocity, v ? Electron Gun