Loading Assignment

Set EVCC5: Cylinder with Constant Charge Density

Problem
Points
1
0/11
2
0/13
3
0/12
Total Score
0/36
Percentage
0 %
Assignment Overview
 1. EVCc5Q1
Points: 0/11

A 12.6 cm radius, 29.5 cm long, non-conductive solid cylinder is charged with 7.9 nC distributed at constant charge density throughout. A 16.6 cm radius, 10.5 cm long Gaussian Surface is drawn surrounding the cylinder as shown at right. An Electric field vector produced by the charged cylinder and 3 dA vectors applied to the Gaussian surface are also shown. Only consider the E-field produced perpedicular to the curved side of the cylinder.

εo=8.85418782*10-12 farads/meter

  1. What is the linear charge density, λ, along the axis of the cylinder?

    Linear Charge Density

    nC/m

    Attempts: 0

  2. How much charge is enclosed in the Gaussian Surface if its length is 10.5 cm?

    Enclosed Charge

    nC

    Attempts: 0

  3. What is the algebraic expression for the E•dA vector dot product after integration for the dA vector pointing out of either flat end of the Gaussian Surface cylinder?

    Attempts: 0

  4. What is the algebraic expression for the E•dA vector dot product after integration for the dA vector pointing out of the curved side of the Gaussian Surface cylinder?

    Attempts: 0

  5. What is the overall algebraic expression for the E•dA vector dot product from all 3 dA vectors after integration?

    Attempts: 0

  6. Integrate Gauss' Law in order to solve for the Electric Field at any position r > R outside the cylinder. Doing this results in the equation E = λ*ra/(2πεo). What is the value of a?

    Attempts: 0

  7. What is the value of the Electric Field at the position of the Gaussian surface?

    E-field

    N/C

    Attempts: 0

  8. What is the value of the Electric Field at the outer surface of the cylinder?

    E-field

    N/C

    Attempts: 0

  9. Assume the Electric Potential at a distance of 100*R from the center of the cylinder is equal to 0. Integrate the relationship E= -dV/dr in order to solve for the Electric Potential at any position R < r < 100*R outside the cylinder. Doing this results in the equation Vr = λ/(2πεo)*ln{(100*R)a*rb}. What are the values of a and b?

    Attempts: 0

  10. What is the Electric Potential at the position of the Gaussian Surface?

    Electric Potential

    Volts

    Attempts: 0

  11. What is the Electric Potential at the surface of the charged cylinder?

    Electric Potential

    Volts

    Attempts: 0
 2. EVCc5Q2
Points: 0/13

A 12.6 cm radius, 28.0 cm long, non-conductive solid cylinder is charged with 5.3 nC distributed at constant charge density throughout. A 4.6 cm radius, 11.0 cm long Gaussian Surface is drawn inside the cylinder as shown at right (charges not shown). An Electric field vector produced by the charged cylinder and 3 dA vectors applied to the Gaussian surface are also shown. Only consider the E-field produced perpedicular to the curved side of the cylinder.

εo=8.85418782*10-12 farads/meter

  1. What is the linear charge density, λ, along the axis of the cylinder?

    Charge Density

    nC/m

    Attempts: 0

  2. How much charge is enclosed in the Gaussian Surface if its length is 11.0 cm?

    Enclosed Charge

    nC

    Attempts: 0

  3. What is the algebraic expression for the E•dA vector dot product after integration for the dA vector pointing out of either flat end of the Gaussian Surface cylinder?

    Attempts: 0

  4. What is the algebraic expression for the E•dA vector dot product after integration for the dA vector pointing out of the curved side of the Gaussian Surface cylinder?

    Attempts: 0

  5. What is the overall algebraic expression for the E•dA vector dot product from all 3 dA vectors after integration?

    Attempts: 0

  6. Integrate Gauss's Law in order to solve for the Electric Field at any position 0 < r < R inside the cylinder. Doing this results in the equation E = λ*ra*Rb/(2πεo). What are the values of a and b?

    Attempts: 0

  7. What is the value of the Electric Field at the position of the Gaussian surface?

    E-field

    N/C

    Attempts: 0

  8. What is the value of the Electric Field at the outer surface of the cylinder?

    E-field

    N/C

    Attempts: 0

  9. What is the value of the Electric Field at the center of the cylinder?

    E-field

    N/C

    Attempts: 0

  10. Assume the Electric Potential at a distance of 100*R from the center of the cylinder is equal to 0. Integrate the relationship E= -dV/dr in order to solve for the Electric Potential at any position 0 < r < R inside the cylinder using the Electric Potential at R as one of the limits*. Doing this results in the equation Vr = λ/(2πεo)*{ln(100)+0.5*(1-(r/R)a)}. What is the value of a?

    *Note that VR=λ/(2πεo)*ln(100) is the result from the question EVCc5Q1.

    Attempts: 0

  11. What is the Electric Potential at the surface of the charged cylinder?

    Electric Potential

    Volts

    Attempts: 0

  12. What is the Electric Potential at the position of the Gaussian Surface?

    Electric Potential

    Volts

    Attempts: 0

  13. What is the Electric Potential at the center of the cylinder?

    Electric Potential 

    Volts

    Attempts: 0
 3. EVCc5Q3
Points: 0/12

A 5 cm radius, 20 cm long non-conductive solid cylinder is charged with 6 nC distributed at constant charge density throughout. The graph of Electric Field and Electric Potential magnitudes versus radial distance from the center of a cylinder with those values is shown at right. Consider the case where the charge is 9.0 nC, the radius of the cylinder is 6.0 cm, and the cylinder length is 28.5 cm. Only consider the E-field produced perpedicular to the curved side of the cylinder.

εo=8.85418782*10-12 farads/meter

  1. Where is the Electric Field equal to zero?

    Attempts: 0

  2. Where is the maxium value of the Electric Field?

    Attempts: 0

  3. What is the maxium value of the Electric Field?

    Electric Field

    N/C

    Attempts: 0

  4. Where is the Electric Potential equal to zero?

    Attempts: 0

  5. Where is the maxium value of the Electric Potential?

    Attempts: 0

  6. What is the maxium value of the Electric Potential?

    Electric Potential

    Volts

    Attempts: 0

  7. Imagine a point P at a certain distance from the center line of the cylinder beyond the outer surface. If I change the position of point P by a factor of 2.60, by how much would the Electric Field magnitude change at point P?

    Factor

    Attempts: 0

  8. Imagine a point P at a distance of 4*R from the center line of the cylinder. If I change the position of point P by a factor of 2.60, by how much would the Electric Potential magnitude change at point P?

    Factor

    Attempts: 0

  9. Imagine a point P at a certain distance from the center line of the cylinder beyond the outer surface. If I change the charge on the cylinder by a factor of 1.35, by how much would the Electric Field magnitude change at point P?

    Factor

    Attempts: 0

  10. Imagine a point P at a distance of 4*R from the center line of the cylinder. If I change the charge on the cylinder by a factor of 1.35, by how much would the Electric Potential magnitude change at point P?

    Factor

    Attempts: 0

  11. Imagine a point P at a certain distance from the center line of the cylinder beyond the outer surface. If I change the charge on the cylinder by a factor of 1.35 and the position by a factor of 2.60, by how much would the Electric Field magnitude change at point P?

    Factor

    Attempts: 0

  12. Imagine a point P at a distance of 4*R from the center line of the cylinder. If I change the charge on the cylinder by a factor of 1.35 and the position by a factor of 2.60, by how much would the Electric Potential magnitude change at point P?

    Factor

    Attempts: 0

Tired of Ads?
Go ad-free for 1 year