Lesson test: Flux and Gauss's law

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Flux and Gauss's law

1.[2p]
Why does the flux of a point charge through a surrounding sphere not depend on the sphere's radius?

The field falls as one over r squared while the area grows as r squared, and the two cancel exactly

Correct

Because flux is defined so as to be constant

The answer is: The field falls as one over r squared while the area grows as r squared, and the two cancel exactly

Because the charge is at the centre, so every radius is equivalent

The answer is: The field falls as one over r squared while the area grows as r squared, and the two cancel exactly

Because $ε_{0}$ has units that absorb the radius

The answer is: The field falls as one over r squared while the area grows as r squared, and the two cancel exactly

2.[2p]
A charge of $5.0$ μC sits inside an irregular closed surface. What is the total electric flux out of it, in units of $10^{5}$ N m² C⁻¹?

CorrectNot quite: 5.65

3.[2p]
A charge outside a closed surface contributes nothing to the field at points on that surface.

True

The answer is: False

False

Correct

4.[3p]
A ball of radius 20 cm carries 80 nC spread uniformly through its volume. What is the field at 10 cm from the centre, in newtons per coulomb?

CorrectNot quite: 8988

5.[2p]
Inside the material of a conductor in electrostatic equilibrium the field is zero because

any field would keep pushing the free charges, so equilibrium would not have been reached

Correct

metals contain no charge to produce a field

The answer is: any field would keep pushing the free charges, so equilibrium would not have been reached

the field is cancelled by the positive ions of the lattice

The answer is: any field would keep pushing the free charges, so equilibrium would not have been reached

Gauss's law forbids a field inside any closed surface

The answer is: any field would keep pushing the free charges, so equilibrium would not have been reached

6.[3p]
A charge of $- 9.0$ nC sits at the centre of a hollow conducting shell carrying a net charge of $+ 5.0$ nC. What charge, in nanocoulombs, ends up on the shell's outer surface? Give the signed value.

CorrectNot quite: -4.0

7.[3p]
The bound on the exponent in Coulomb's law comes from looking for charge inside a hollow charged conductor rather than from measuring forces because

the prediction is exactly zero, and zero can be tested to arbitrary precision without a calibration

Correct

forces between charges are too large to measure accurately

The answer is: the prediction is exactly zero, and zero can be tested to arbitrary precision without a calibration

the interior of a conductor is easier to reach than its surface

The answer is: the prediction is exactly zero, and zero can be tested to arbitrary precision without a calibration

flux cannot be measured directly

The answer is: the prediction is exactly zero, and zero can be tested to arbitrary precision without a calibration

8.[3p]
For which of these does Gauss's law let you find the field without doing a vector integral?

Select all that apply

A uniformly charged sphere

Correct

A very long straight charged wire

Correct

A large uniformly charged flat sheet

Correct

A uniformly charged cube

The answer is: A uniformly charged sphere, A very long straight charged wire, A large uniformly charged flat sheet

9.[3p]
Match each situation to the field it produces.

Isolated charged sheet
Just outside a conductor
Long line at distance r
Inside the metal of a conductor

sigma over two epsilon nought
zero
sigma over epsilon nought
lambda over two pi epsilon nought r

Show the answer

Isolated charged sheet: sigma over two epsilon nought Just outside a conductor: sigma over epsilon nought Long line at distance r: lambda over two pi epsilon nought r Inside the metal of a conductor: zero

1.[2p] Why does the flux of a point charge through a surrounding sphere not depend on the sphere's radius?

2.[2p] A charge of 5.0 μC sits inside an irregular closed surface. What is the total electric flux out of it, in units of 105 N m² C⁻¹?

3.[2p] A charge outside a closed surface contributes nothing to the field at points on that surface.

4.[3p] A ball of radius 20 cm carries 80 nC spread uniformly through its volume. What is the field at 10 cm from the centre, in newtons per coulomb?

5.[2p] Inside the material of a conductor in electrostatic equilibrium the field is zero because

6.[3p] A charge of -9.0 nC sits at the centre of a hollow conducting shell carrying a net charge of +5.0 nC. What charge, in nanocoulombs, ends up on the shell's outer surface? Give the signed value.

7.[3p] The bound on the exponent in Coulomb's law comes from looking for charge inside a hollow charged conductor rather than from measuring forces because

8.[3p] For which of these does Gauss's law let you find the field without doing a vector integral?

9.[3p] Match each situation to the field it produces.

1.[2p]
Why does the flux of a point charge through a surrounding sphere not depend on the sphere's radius?

2.[2p]
A charge of $5.0$ μC sits inside an irregular closed surface. What is the total electric flux out of it, in units of $10^{5}$ N m² C⁻¹?

3.[2p]
A charge outside a closed surface contributes nothing to the field at points on that surface.

4.[3p]
A ball of radius 20 cm carries 80 nC spread uniformly through its volume. What is the field at 10 cm from the centre, in newtons per coulomb?

5.[2p]
Inside the material of a conductor in electrostatic equilibrium the field is zero because

6.[3p]
A charge of $- 9.0$ nC sits at the centre of a hollow conducting shell carrying a net charge of $+ 5.0$ nC. What charge, in nanocoulombs, ends up on the shell's outer surface? Give the signed value.

7.[3p]
The bound on the exponent in Coulomb's law comes from looking for charge inside a hollow charged conductor rather than from measuring forces because

8.[3p]
For which of these does Gauss's law let you find the field without doing a vector integral?

9.[3p]
Match each situation to the field it produces.