A thin spherical shell made of plastic carries a uniformly distributed negative

Question

A thin spherical shell made of plastic carries a uniformly distributed negative charge -5e-10 coulombs (indicated as -Q1 in the diagram). Two large thin disks made of glass carry uniformly distributed positive and negative charges 1.3e-05 coulombs and -1.3e-05coulombs (indicated as +Q2 and -Q2 in the figure). The radius R1 of the plastic spherical shell is 6 mm, and the radius R2 of the glass disks is 4 meters. The distance d from the center of the spherical shell to the positive disk is 19 mm.

A thin spherical shell made of plastic carries a uniformly distributed negative charge -5e-10 coulombs (indicated as -Q1 in the diagram). Two large thin disks made of glass carry uniformly distributed positive and negative charges 1.3e-05 coulombs and -1.3e-05coulombs (indicated as +Q2 and -Q2 in the figure). The radius R1 of the plastic spherical shell is 6 mm, and the radius R2 of the glass disks is 4 meters. The distance d from the center of the spherical shell to the positive disk is 19 mm Find the potential difference V1 - V2. Point 1 is at the center of the plastic sphere, and point 2 is just outside the sphere. Find the potential difference V2 - V3. Point 2 is just below the sphere, and point 3 is right beside the positive glass disk.

Explanation / Answer

GIVEN THESE INITIAL VALUES (which we are):
e = 8.85*10^-12; ..............EPSILON CONSTANT
Qsphere = -6*10^-10; ...............CHARGE ON SPHERE
QC = 1.3*10^-5; ................... CHARGE ON POSITIVE DISK
R1 = .006; ............. RADIUS OF SPHERE IN METERS
R2 = 4; ................RADIUS OF DISK IN METERS
D = .017;..............DISTANCE FROM DISK TO CENTER OF SPHEREIN METERS

First_ANSWER_1 A)=-(QC/(pi*(R2^2))/e)*R1

OTENTIAL DIFFERENCE FOR Sphere =((9*10^9)*((Qsphere/D)-(Qsphere/R1)))
POTENTIAL DIFFERENCE FOR Disk=(QC/(pi*(R2^2))/e)*(D-R1)

therefore,

FINAL_ANSWER_2 = -(((9*10^9)*((Qsphere/D)-(Qsphere/R1))) +(QC/(pi*(R2^2))/e)*(D-R1))
(THIS IS POTENTIAL DIFFERENCE OF THE SPHERE PLUS (+) the DISK)

***NOTE*** THE DISKS POTENTIAL DIFFERENCE IN THE SECOND ANSWER ISCOMPLETELY DIFFERENT FROM THE POTENTIAL DIFFERENCE IN ANSWER 1, SODO NOT USE ANSWER A) for PART B).

ALSO NOTICE THAT THE POTENTIAL DIFFERENCE IS NEGATIVE (-) IN BOTHCASES.
THIS IS BECAUSE THE ELECTRIC FIELD POINTS UPWARD, AND YOU ARESTARTING FROM THE BOTTOM AND MOVING IN THE POSITIVE (+) y DIRECTIONFOR YOUR DISTANCE TRAVELED (R) OR (D). SO THE ELECTRIC FIELD ANDYOUR DELTA L (length or distance traveled) ARE BOTH POINTING IN THESAME DIRECTION.

FOR THIS PARTICULAR PROBLEM:

A) = -175 V

AND

B) = -951.4139

with the DISK potential difference V3-V2 = -272.0021

and the SPHERE potential difference from V3-V2 = -679.4118

add together to get B) = -951.4139

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