PHY 2049: Physics II Hopefully all homework problems have been solved. Please see me immediately after the class if there is still an issue. Tea and Cookies: We meet on Wednesdays at 4:00PM for tea and cookies in room 2165.

quiz The electric field at a distance of 10 cm from an isolated point particle with a charge of 2×10 −9 C is: A. 1.8N/CB. 180N/CC. 18N/C D. 1800N/CE. none of these

Quiz 2 An isolated charged point particle produces an electric field with magnitude E at a point 2m away from the charge. A point at which the field magnitude is E/4 is: A. 1m away from the particle B. 0.5m away from the particle C. 2m away from the particle D. 4m away from the particle E. 8m away from the particle

PHY 2049: Physics II Last week Coulomb’s law, Electric Field and Gauss’ theorem Today Electric Potential Energy and Electric Potentials Numerous cases

Potential Energy and Potential Force => work => change in K=> change in Potential energy ΔU = U f – U i = -W = - ΔK Work done is path independent. K+U = constant. U = k q 1 q 2 /r : interaction energy of two charges. Sign matters

PHY 2049: Physics II Electric Potential V = U/q = -W/q Units of Joules/coulomb = volt 1 eV = e x 1V = 1.6 x J Also V = kq/r V f –V i = -∫E.ds In case of multiple charges, add as a number

PHY 2049: Physics II Can you tell the sign of the charge by looking at its behavior over a surface of potentials. Is the speed at the end bigger or smaller than in the beginning. 1.Neg., lower 2.? 3.Pos., higher 4.Neg., higher 5.Pos., higher

PHY 2049: Physics II V f -V i = -∫ k q/r 2 dr Choose V i = V (∞)=0 V(r) = kq/r

V = kpcosθ/r 2 E = - ∂V/∂s = - Uniformly charged disk V = ??

A B C (24 - 6)

dq O A (24 - 8)

PHY 2049: Physics II

. P r dq (24 - 7)

(24 - 9)

( )

S A B  V q ( ) S V

( )

A B V V+dV ( )

A B V V+dV ( )

x y O q1q1 q2q2 q3q3 r 12 r 23 r 13 ( )

( ) O x y  q1q1 Step 1 x y O r 12 q1q1 q2q2  Step 2 Step 3 x y O r 12 r 13 r 23 q1q1 q2q2 q3q3 

path A B conductor ( )

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R ( )