Problem #1: A flat sheet of paper of area 0.260m2 is oriented so that the normal to the sheet is at an angle of 61∘ to a uniform electric field of magnitude 12N/C.

Part A: Find the magnitude of the electric flux through the sheet.

Part B: Does the answer to part A depend on the shape of the sheet?

Part C: For what angle 

ϕ between the normal to the sheet and the electric field is the magnitude of the flux through the sheet largest?

Part D: For what angle 

ϕ between the normal to the sheet and the electric field is the magnitude of the flux through the sheet smallest?

Part E: Explain your answers in parts C and D.

Problem #2: You measure an electric field of 1.28×106

N/C at a distance of 0.157m from a point charge. There is no other source of electric field in the region other than this point charge.

Part A: What is the electric flux through the surface of a sphere that has this charge at its center and that has radius 0.157

m ?

Part B: What is the magnitude of the charge?

Problem #3: A point charge of +8.00

μC is located on the x-axis at x= 6.00m , next to a spherical surface of radius x= 5.00m centered at the origin.

Part A:Calculate the magnitude of the electric field at 

x= 5.00m . 

Part B: Calculate the magnitude of the electric field at 

x= -5.00m .

Problem #4: A solid metal sphere with radius 0.470

m carries a net charge of 0.250nC .

Part A: Find the magnitude of the electric field at a point 0.114

m outside the surface of the sphere.

Part B: Find the magnitude of the electric field at a point inside the sphere, 0.114

m below the surface.

Problem #5: Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of 3.59×1016

N⋅m2/C into the planet’s surface.

Part A: Calculate the total electric charge on the planet.

Part B: Calculate the magnitude of the electric field at the planet’s surface

Part C: Find the direction of the electric field at the planet’s surface.

Part D: Calculate the charge density on Mars, assuming all the charge is uniformly distributed over the planet’s surface.

 Problem #6: The three small spheres shown in the figure 

carry charges q1 = 3.65nC , q2 = -7.80nC , and q3 = 2.75nC .

Part A: Find the net electric flux through the closed surface 

S1 shown in cross section in the figure.

Part B: Find the net electric flux through the closed surface 

S2 shown in cross section in the figure.

Part C: Find the net electric flux through the closed surface 

S3 shown in cross section in the figure.

Part D: Find the net electric flux through the closed surface 

S4 shown in cross section in the figure.

Part E: Find the net electric flux through the closed surface 

S5 shown in cross section in the figure.

Part F:Do your answers to parts A through E depend on how the charge is distributed over each small sphere?

Part G: Why or why not?

Problem #1: A flat sheet of paper of area 0.260m2 is oriented so that the normal to the sheet is at an angle of 61∘ to a uniform electric field of magnitude 12N/C.

Part A: Find the magnitude of the electric flux through the sheet.

Part B: Does the answer to part A depend on the shape of the sheet?

Part C: For what angle 

ϕ between the normal to the sheet and the electric field is the magnitude of the flux through the sheet largest?

Part D: For what angle 

ϕ between the normal to the sheet and the electric field is the magnitude of the flux through the sheet smallest?

Part E: Explain your answers in parts C and D.

Problem #2: You measure an electric field of 1.28×106

N/C at a distance of 0.157m from a point charge. There is no other source of electric field in the region other than this point charge.

Part A: What is the electric flux through the surface of a sphere that has this charge at its center and that has radius 0.157

m ?

Part B: What is the magnitude of the charge?

Problem #3: A point charge of +8.00

μC is located on the x-axis at x= 6.00m , next to a spherical surface of radius x= 5.00m centered at the origin.

Part A:Calculate the magnitude of the electric field at 

x= 5.00m . 

Part B: Calculate the magnitude of the electric field at 

x= -5.00m .

Problem #4: A solid metal sphere with radius 0.470

m carries a net charge of 0.250nC .

Part A: Find the magnitude of the electric field at a point 0.114

m outside the surface of the sphere.

Part B: Find the magnitude of the electric field at a point inside the sphere, 0.114

m below the surface.

Problem #5: Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of 3.59×1016

N⋅m2/C into the planet’s surface.

Part A: Calculate the total electric charge on the planet.

Part B: Calculate the magnitude of the electric field at the planet’s surface

Part C: Find the direction of the electric field at the planet’s surface.

Part D: Calculate the charge density on Mars, assuming all the charge is uniformly distributed over the planet’s surface.

 Problem #6: The three small spheres shown in the figure 

carry charges q1 = 3.65nC , q2 = -7.80nC , and q3 = 2.75nC .

Part A: Find the net electric flux through the closed surface 

S1 shown in cross section in the figure.

Part B: Find the net electric flux through the closed surface 

S2 shown in cross section in the figure.

Part C: Find the net electric flux through the closed surface 

S3 shown in cross section in the figure.

Part D: Find the net electric flux through the closed surface 

S4 shown in cross section in the figure.

Part E: Find the net electric flux through the closed surface 

S5 shown in cross section in the figure.

Part F:Do your answers to parts A through E depend on how the charge is distributed over each small sphere?

Part G: Why or why not?