Remember to show ALL of your work, you may recieve partial credit. Also, please

Question

Remember to show ALL of your work, you may recieve partial credit. Also, please underline or circle your final answers. Good luck! 1) A conducting sphere of radius R carries an excess positive charge and is very far from any other charges. Which one of the following graphs best illustrates the potential (relative to infinity) produced by this sphere as a function of the distancer from the center of the sphere? 2) Two large conducting parallel plates A and B with areas of 400mm^2 are separated by 2.4 mm of vaccum (K=1.00). A uniform field of 1500 V/m, in the positive x-direction, is produced by charges on the plates. The center plane at x = 0.00 m is an equipotential surface on which V = 0. An electron is projected from x = 0.00 m, With an initial velocity of 1.0 x 10 m/s perpendicular to the plates in the positive x-direction, as shown in the figure. = 1.60 x 10^-19 C, m_el = 9.11 x 10^31 kg) (a) What is the capacitance? (b) What it the surface charge density on each plate? (c) What is the kinetic energy of the electron as it reaches plate A?

Explanation / Answer

1. variation of potential of with distance uis given as shown in figure C

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2a. Capaciatnce C = eo A/d

C = 8.85 e -12 * 400 e -6/(2.4 e -3)

C = 1.475 pF

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part B :

surface charge density sigma = Q/A

charge Q = CV

but E = V/d ---> V = Ed

so

Q = CEd

Q = 1.475 e -12 * 1500 * 2.4 e -3

Q = 5.31 pC

sigma = 5.31 e -12/(400 e-6)

sigma = 13.2 nC/m^2

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part C :

use ma = Eq

a = 1500* 1.6 e-19/ 9.11 e -31

a = 2.63 e 14 m/s^2

distance travelled from x= 0 to 1.2 m is 1.2 m

so use v^2 = 2aS

V^2 = 2* 2.63 e 14 * 1.2

V^2 = 6.312e+14 (m/s)^2

so

KE = 0.5 mv^2

KE = 0.5* 9.11 e -31 * 6.34 e 14

KE = 2.88 *!0^-16 J

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