Question

trina makes a diagram to summarize how to use the right-hand rule to determine the direction of the magnetic force on each type of charge.
diagram: two overlapping circles labeled
egative\ (x in only negative region) and \positive\ (z in only positive region), y in the overlapping region.
which labels belong in the regions marked x, y, and z?

• x: thumb, for velocity

y: fingers, for magnetic field
z: palm of hand, for force

• x: back of hand, for force

y: thumb, for velocity
z: palm of hand, for force

• x: palm of hand, for force

y: thumb, for velocity
z: fingers, for magnetic field

• x: palm of hand, for force

y: fingers, for magnetic field
z: back of hand, for force

Explanation:

To determine the labels for X, Y, Z using the right - hand rule for magnetic force on charges:

1. Recall the right - hand rule for positive charges: Thumb (velocity), Fingers (magnetic field), Palm (force). For negative charges, the force direction is opposite, so we use the back of the hand for force (equivalent to reversing the palm direction).
2. Region Y is the overlap (applies to both positive and negative charges). For both, the thumb represents velocity and fingers represent the magnetic field (this is the common part of the rule for charge - magnetic force interaction).
3. Region X is only for negative charges: The force direction is given by the back of the hand? No, wait, let's re - analyze. Wait, the right - hand rule for positive charge: thumb (v), fingers (B), palm (F). For negative charge, since \( \vec{F}=-q(\vec{v}\times\vec{B}) \) (if \( q>0 \) for positive, \( q < 0 \) for negative), the force on negative charge is opposite to positive. So for negative charge, we can use the left - hand rule or use the right - hand rule and then reverse the force direction. But in terms of the Venn diagram:

• Y is the intersection (applies to both positive and negative). So Y should be thumb (velocity) and fingers (magnetic field) (the part common to both charge types for the rule's basic hand positions for v and B).
• X is only negative: For negative charge, the force is indicated by the back of the hand (since for positive it's the palm). Wait, no, let's check the options.
• Let's analyze each option:
• Option 1: X: Thumb (v) – no, thumb is for velocity in both, but X is only negative. So wrong.
• Option 2: X: Back of hand (force) – for negative charge, force is opposite to positive. Positive uses palm for force, so negative uses back of hand. Y: Thumb (v) – thumb is for velocity (common to both). Z: Palm of hand (force) – for positive charge. This matches the right - hand rule: For positive, thumb (v), fingers (B), palm (F); for negative, thumb (v), fingers (B), back of hand (F) (since force is opposite). So Y (intersection) is thumb (v) and fingers (B) (common), X (negative only) is back of hand (force), Z (positive only) is palm of hand (force).
• Option 3: X: Palm (force) – no, palm is for positive. Wrong.
• Option 4: X: Palm (force) – wrong, palm is positive. Y: Fingers (B) – but thumb is for velocity. Wrong.

Answer:

X: Back of hand, for force
Y: Thumb, for velocity
Z: Palm of hand, for force (the second option in the given choices)