Questions: A Gaussian cylinder is drawn around some hidden charges, as shown in the figure below.
Part 1
Given this pattern of electric field on the surface of the cylinder, how much net charge is inside?
- The quantity cannot be measured, but the net charge is negative; there is twice the amount of negative charge inside as positive charge.
- The quantity cannot be measured, but the net charge is positive; there is twice the amount of positive charge inside as negative charge.
- The net charge is zero.
Save for Later
Attempts: 0 of 6 used
Submit Answer
Using multiple attempts will impact your score.
40% score reduction after attempt 3
Part 2
Invent a possible charge distribution inside the cylinder that could give this pattern of electric field.
- a point charge
- a uniformly charged ring, which shares a central axis with the cylinder
- a dipole, with the positive charge on the left end of the cylinder
- a dipole, with the positive charge on the right end of the cylinder
- a uniformly charged rod
Transcript text: A Gaussian cylinder is drawn around some hidden charges, as shown in the figure below.
Part 1
Given this pattern of electric field on the surface of the cylinder, how much net charge is inside?
The quantity can not be measured, but the net charge is negative; there is twice the amount of negative charge inside as positive charge.
The quantity can not be measured, but the net charge is positive; there is twice the amount of positive charge inside as negative charge.
The net charge is zero.
Save for Later
Attempts: 0 of 6 used
Submit Answer
Using multiple attempts will impact your score.
$40 \%$ score reduction after attempt 3
Part 2
Invent a possible charge distribution inside the cylinder that could give this pattern of electric field.
a point charge
a uniformly charged ring, which shares a central axis with the cylinder
a dipole, with the positive charge on the left end of the cylinder
a dipole, with the positive charge on the right end of the cylinder
a uniformly charged rod
Solution
Solution Steps
Step 1: Apply Gauss's Law
Gauss's Law states that the electric flux through a closed surface is proportional to the enclosed charge. The electric field lines are pointing radially outwards from the cylindrical surface. This indicates a net positive charge within the Gaussian surface. Since the field lines are uniform and radially outward, the net flux through the surface is positive and constant.
Step 2: Determine the net charge
Because the electric field lines are directed outward and symmetrical across the Gaussian surface, this tells us there is a net charge enclosed and it is positive.
Step 3: Possible charge distribution
A dipole with the positive charge on the right end of the cylinder could produce the outward-pointing electric field depicted.
Final Answer:
Part 1: The net charge is positive.
Part 2: A dipole, with the positive charge on the right end of the cylinder.