Supervillain Prof. Marcia Grail is experimenting with energy and electric charge

Question

Supervillain Prof. Marcia Grail is experimenting with energy and electric charge to better create a new doomsday weapon (and take over the world). She gathers a charge of 1.11 x 10^-10 C and places it in the center of a large empty spherical vacuum chamber of radius 250m (the place she fixes this immovable charge can be thought of as the origin of coordinates). The potential at a point 1m away in the positive y-direction is 1 V. What is the potential 1m away in the positive x-direction? If she then places a movable particle with mass 2 micrograms and a charge of +2 Coulombs at the point 1m away in the positive y-direction, how much energy is stored in this configuration (assume that the outer surface of the vacuum chamber is the zero of potential energy)?

Explanation / Answer

given

charge of 1.11 x 10^-10 C

radius 250m

The potential at a point 1m

and 1 V

mass 2 micrograms

charge of +2 Coulombs

the potential is V = K Q / r

V = 9 X 109 X 1.11 X 10-10 / 1

V = 9 X 109 X 1.11 X 10-10

V = 0.999 volt

nearly it is V = 1 v

the energy stored is U = q X V

U = 2 X 1

U = 2 J

the energy is stored in this configuration is U = 2 J

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