Question

module 2a
visualizing electric fields
to understand the nature of electric fields and how to draw
field lines
electric field lines are a tool used to visualize electric
fields. a field line is drawn beginning at a positive charge
and ending at a negative charge. field lines may also
appear from the edge of a picture or disappear at the edge
of the picture. such lines are said to begin or end at
infinity. the field lines are directed so that the electric field
at any point is tangent to the field line at that point
figure
3 of 4
in (figure 2), what is wrong with panel b? (pick only those statements that apply to panel b.)
check all that apply.
field lines cannot cross each other.
the field lines should be parallel because of the sheet’s symmetry.
the field lines should spread apart as they leave the sheet to indicate the weakening of the field with distance.
the field lines should always end on negative charges or at infinity.
submit previous answers request answer
incorrect; try again; 2 attempts remaining
recall that the field around an infinite charged sheet is always perpendicular to the sheet and that the field strength does not change,
regardless of distance from the sheet.
part c
which of the following panels (labelled a, b, c, and d) in (figure 3) shows the correct electric field lines for an electric dipole?

Answer:

1. For the first option "Field lines cannot cross each other": Looking at panel B, we check if field lines cross. From the context (even though the figure is partially shown, the problem is about electric field lines of a dipole? Wait, no, the hint mentions infinite charged sheet? Wait, no, the figure has A, B (with two charges, maybe dipole) and C, D (with a sheet? Wait, the hint says "the field around an infinite charged sheet is always perpendicular to the sheet and that the field strength does not change, regardless of distance from the sheet." Wait, maybe panel B is for a dipole? No, maybe the first part is about a charged sheet? Wait, no, the question is about panel B. Let's re-examine the options:

• "Field lines cannot cross each other": If panel B has crossing field lines, but maybe not. Wait, the hint says "the field around an infinite charged sheet is always perpendicular to the sheet and that the field strength does not change, regardless of distance from the sheet." So for an infinite charged sheet, the electric field lines should be parallel (since field is uniform, same strength everywhere, so lines are parallel, not spreading). Also, field lines for a sheet are perpendicular to the sheet. Wait, maybe panel B is supposed to represent the field from an infinite sheet? No, the figure has two charges (like a dipole) in A and B, and a sheet with two charges? Wait, maybe the first part (panel B) is for a dipole? No, the hint is about infinite charged sheet. Wait, the options:

• "The field lines should be parallel because of the sheet’s symmetry": For an infinite charged sheet, the electric field is uniform, so field lines are parallel (since E is constant in magnitude and direction, so lines are parallel, equally spaced). If panel B's field lines are not parallel (maybe curving or spreading), this would be wrong.

• "The field lines should spread apart as they leave the sheet to indicate the weakening of the field with distance": But for an infinite sheet, the field strength is independent of distance (E = σ/(2ε₀) for infinite sheet, uniform), so field lines should not spread. So this statement is wrong (the field doesn't weaken with distance, so lines shouldn't spread), but is this a problem with panel B? Wait, the hint says "the field strength does not change, regardless of distance from the sheet", so if panel B shows lines spreading, that's wrong. But also, "The field lines should be parallel because of the sheet’s symmetry" – if the sheet is infinite, lines should be parallel.

Wait, maybe the first question (panel B) is about a dipole? No, the hint is about infinite sheet. Wait, the user's question is about panel B: what's wrong. Let's analyze each option:

1. "Field lines cannot cross each other": If panel B has crossing lines, but maybe not. Let's assume the figure for panel B (maybe with two charges, a dipole? No, the hint is about infinite sheet. Wait, maybe the figure has a sheet (like a horizontal line) and two charges? No, the left figure (A and B) have two charges (blue and red, like + and -), and C and D have a horizontal sheet with two charges below? Wait, maybe panel B is supposed to represent the field from an infinite sheet, but the lines are not parallel. Or maybe it's a dipole? No, the hint is about infinite sheet.

Wait, the correct options: From the hint, "the field around an infinite charged sheet is always perpendicular to the sheet and that the field strength does not change, regardless of distance from the sheet." So:

• "The field lines should be parallel because of the sheet’s symmetry": Correct, because infinite sheet has uniform field, so lines are parallel. If panel B's lines are not parallel (e.g., curving or spreading), this is wrong.

• "The field lines should spread apart as they leave the sheet to indicate the weakening of the field with distance": Wrong, because field doesn't weaken, so lines shouldn't spread. So if panel B shows lines spreading, this is a mistake. But wait, the hint says "the field strength does not change", so this statement is incorrect (the field doesn't weaken, so lines shouldn't spread), so if panel B has lines spreading, this is wrong. But also, "The field lines should be parallel..." is correct as a mistake in panel B.

Wait, maybe the first option "Field lines cannot cross each other" – if panel B has crossing lines, but maybe not. Let's re-express:

For an infinite charged sheet, electric field lines are:

• Perpendicular to the sheet (if the sheet is, say, horizontal, lines are vertical).

• Parallel (since E is uniform, same direction and magnitude everywhere, so lines are parallel, equally spaced, no spreading).

So in panel B, if the lines are not parallel (e.g., curving or spreading), then "The field lines should be parallel because of the sheet’s symmetry" is a mistake in panel B. Also, "The field lines should spread apart as they leave the sheet to indicate the weakening of the field with distance" is wrong (since field doesn't weaken), so if panel B shows spreading, this is wrong. But the hint says "the field strength does not change, regardless of distance from the sheet", so the second option (parallel) and the third (spreading) – wait, the third option says "should spread apart" which is wrong, so if panel B has spreading, that's a mistake. But maybe the correct options are "The field lines should be parallel because of the sheet’s symmetry" and "The field lines should spread apart...". Wait, no: the field around an infinite sheet is uniform, so lines are parallel (not spreading), so panel B is wrong if lines are not parallel (so "should be parallel" is a correct criticism) and if lines are spreading (so "should spread apart" is a wrong statement, but the problem is what's wrong with panel B – so if panel B has lines that are not parallel (so "should be parallel" is a mistake in panel B) and/or lines that spread (so "should spread apart" is a wrong thing panel B is doing).

Wait, the initial incorrect attempt: the user got it wrong, and the hint says to recall that the field around an infinite charged sheet is always perpendicular to the sheet and field strength doesn't change with distance. So:

• "The field lines should be parallel because of the sheet’s symmetry": Correct, because infinite sheet has translational symmetry, so field is uniform, lines are parallel. If panel B's lines are not parallel, this is wrong.

• "The field lines should spread apart as they leave the sheet to indicate the weakening of the field with distance": Wrong, because field doesn't weaken, so lines shouldn't spread. So if panel B shows lines spreading, this is a mistake.

• "Field lines cannot cross each other": If panel B has crossing lines, but maybe not. Let's assume the figure for panel B (maybe with two charges, but the hint is about infinite sheet). Wait, maybe the figure has a sheet (horizontal line) and two charges (like a dipole) above? No, the left figure (A and B) have two charges (blue and red) with field lines, and C and D have a horizontal sheet with two charges below, field lines going up/down.

Wait, maybe panel B is for a dipole? No, the hint is about infinite sheet. I think the correct options are "The field lines should be parallel because of the sheet’s symmetry" and "The field lines should spread apart as they leave the sheet to indicate the weakening of the field with distance" – no, wait, the field around an infinite sheet is uniform, so lines are parallel (not spreading), so panel B is wrong if lines are not parallel (so "should be parallel" is a criticism) and if lines are spreading (so "should spread apart" is a wrong action, so the statement "The field lines should spread apart..." is a wrong thing that panel B is doing? No, the statement is a description of what's wrong with panel B: if panel B has lines spreading, then the statement "The field lines should spread apart..." is not a correct criticism (because they shouldn't spread), so the mistake in panel B is that lines spread, so the statement "The field lines should spread apart..." is not a correct reason, but the problem is to check which statements apply (i.e., which statements are true about what's wrong with panel B).

Wait, let's rephrase:

• "Field lines cannot cross each other": If panel B has crossing lines, this is wrong. But maybe not.

• "The field lines should be parallel because of the sheet’s symmetry": For an infinite sheet, field lines are parallel (uniform field), so if panel B's lines are not parallel, this is a mistake. So this statement applies (i.e., panel B is wrong because lines are not parallel, so they should be parallel).

• "The field lines should spread apart as they leave the sheet to indicate the weakening of the field with distance": For an infinite sheet, field doesn't weaken, so lines shouldn't spread. So if panel B's lines spread, this is a mistake. So this statement applies (i.e., panel B is wrong because lines spread, which they shouldn't, as field doesn't weaken).

• "The field lines should always end on negative charges or at infinity": For an infinite sheet, field lines are perpendicular, starting from positive sheet (if sheet is positive) or ending on negative sheet. But maybe panel B has lines not ending correctly, but the hint is about parallel and spreading.

Given the hint: "Recall that the field around an infinite charged sheet is always perpendicular to the sheet and that the field strength does not change, regardless of distance from the sheet." So the key points are:

• Field is perpendicular to the sheet (so lines should be perpendicular, maybe parallel if sheet is flat).

• Field strength is constant (so lines should be parallel, not spreading).

So the mistakes in panel B are:

• Lines are not parallel (so "The field lines should be parallel because of the sheet’s symmetry" applies).

• Lines spread apart (so "The field lines should spread apart as they leave the sheet to indicate the weakening of the field with distance" – but wait, the field doesn't weaken, so lines shouldn't spread, so panel B is wrong to have lines spreading, so this statement is a description of what's wrong (i.e., panel B does spread lines, which is wrong, so the statement "The field lines should spread apart..." is a wrong thing that panel B is doing? No, the statement is a question of whether that's a mistake. So if the field doesn't weaken, then lines shouldn't spread, so panel B is wrong to have lines spreading, so the statement "The field lines should spread apart..." is a mistake in panel B (i.e., panel B does that, which is wrong).

Wait, maybe the correct options are "The field lines should be parallel because of the sheet’s symmetry" and "The field lines should spread apart as they leave the sheet to indicate the weakening of the field with distance" – but no, the field doesn't weaken, so lines shouldn't spread, so the second statement is a wrong action, so panel B is wrong to have lines spreading, so that statement applies (i.e., the mistake is that lines spread, so the statement "The field lines should spread apart..." is a description of the mistake).

But also, "Field lines cannot cross each other" – if panel B has crossing lines, but maybe not. Given the hint, the main points are parallel and no spreading. So the correct options are "The field lines should be parallel because of the sheet’s symmetry" and "The field lines should spread apart as they leave the sheet to indicate the weakening of the field with distance".

Wait, but the initial incorrect attempt: the user checked some options, and the system said to recall about infinite sheet. So let's confirm:

For an infinite uniformly charged sheet, the electric field is:

• Magnitude: \( E = \frac{\sigma}{2\epsilon_0} \) (for non-conducting sheet), uniform (independent of distance).

• Direction: Perpendicular to the sheet (away from positive, towards negative).

So field lines are:

• Parallel (since E is uniform, same direction and magnitude everywhere, so lines are parallel, equally spaced, no curvature, no spreading).

So in panel B, if the field lines are not parallel (e.g., curved or spreading), then:

• "The field lines should be parallel because of the sheet’s symmetry" – correct, panel B is wrong because lines are not parallel.

• "The field lines should spread apart as they leave the sheet to indicate the weakening of the field with distance" – wrong, because field doesn't weaken, so lines shouldn't spread. So if panel B shows lines spreading, this is a mistake, so this statement applies (i.e., panel B is wrong to have lines spreading, so the statement is a description of the mistake).

• "Field lines cannot cross each other" – if panel B has crossing lines, but maybe not. Let's assume the figure for panel B (maybe with two charges, but the hint is about infinite sheet). Maybe the figure has a sheet (horizontal line) and two charges (dipole) above, but the hint is about infinite sheet. I think the correct options are "The field lines should be parallel because of the sheet’s symmetry" and "The field lines should spread apart as they leave the sheet to indicate the weakening of the field with distance".

For the second part (Part C: Which panel shows correct electric field lines for an electric dipole?):

An electric dipole consists of two equal and opposite charges (positive and negative) separated by a distance. The electric field lines:

• Start from the positive charge and end on the negative charge.

• Are curved, forming loops (but not crossing), with lines going from + to - and also some going to/from infinity (but for a dipole, most lines go from + to -).

• The field lines are symmetric with respect to the axis of the dipole (the line connecting the two charges) and the perpendicular bisector.

Looking at the panels (A, B, C, D):

• Panel A: Maybe has lines that start at +, end at -, and are symmetric.

• Panel B: Maybe has crossing lines or incorrect sym…