# 1Bweek7 - Physics 1B Walter Gekelman Capacitors and...

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

1 Physics 1B Class Notes© Week 7 Walter Gekelman Capacitors and Capacitance Consider the potential on axis of a ring of charge (1) V = 1 4 πε 0 Q x 2 + a 2 . X is the distance from the center For a line of charge with charge density (chg/length) λ , and length 2a, the potential at a point x above the center is (2) V = 1 4 0 Q 2 a ln a 2 + x 2 + a a 2 + x 2 a and the potential of a single charge located at the origin as a function of the distance r away from it is (3) V = 1 4 0 Q r The potential between the plates of a parallel plate capacitor (plate area A, seperation between plates d is (4) V = d ε 0 Q A . These all have the form (5) Q = CV where Q is the charge on either plate. Note the quantity C depends only upon the geometry of the object. It is called the capacitance and in mks its unit is the Farad (named in honor of Michael Faraday) For example the parallel plate capacitor

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

View Full Document
2 For a cylindrical capacitor Find the E field from Gauss’s law and then show that : When the charge on a capacitor is increased then the electric field within it increases and it consequently stores more energy. The energy stored, W is: As Q=CV this can be re-written: W = 1 Q 2 2 C = 1 2 C 2 V 2 C = CV 2 2 Capacitors in Series: Consider 2 capacitors in series with a battery across them.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 8

1Bweek7 - Physics 1B Walter Gekelman Capacitors and...

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

View Full Document
Ask a homework question - tutors are online