Question

A moving negative charge placed in an external magnetic field circulates counterclockwise in the plane of the paper. In which direction is the magnetic field pointing? (A) Into the page (B) Out of the page (C) Toward the center of the circle (D) Tangent to the circle

Short answer

The magnetic field is pointing into the page (A).

Step-by-step solution

Identify the Given Information

A negative charge is moving in a counterclockwise direction in the plane of the paper due to an external magnetic field.

Use the Right-Hand Rule for a Negative Charge

For a negative charge moving in a magnetic field, the right-hand rule is modified: Point the thumb in the direction opposite to the motion of the particle (since it is negative).

Determine Thumb Direction

Since the charge is moving counterclockwise, point the thumb of the right hand clockwise.

Identify the Palm Orientation

With the thumb (representing the direction opposite to motion) pointing clockwise, orient the palm perpendicular to the thumb. This orientation will indicate the magnetic field.

Determine the Direction of the Magnetic Field

With the palm facing the direction of the force, the magnetic field points into the page.

Key concepts

right-hand rule

The right-hand rule is a straightforward method to find the direction of the magnetic force. When dealing with a positive charge, you point your thumb in the direction of the charge's velocity. Extend your fingers in the direction of the magnetic field. Your palm will face the direction of the force acting on the charge.
However, for a negative charge, the situation is a bit different.
Point your thumb in the opposite direction of the charge's motion to get the correct force direction.
This adjustment ensures that the rule works correctly regardless of the charge nature.

negative charge

Negative charges behave differently in magnetic fields compared to positive charges.
In our case, a negative charge is following a counterclockwise path due to the magnetic field interaction. We adjust the right-hand rule for negative charges.
Point your thumb in the direction opposite to the actual motion. This compensates for the negative nature of the charge.
Remember, opposite direction for the thumb means correct force direction prediction.

magnetic field orientation

To understand how the magnetic field is influencing the negative charge, we need to correctly interpret the field orientation.
After adjusting the right-hand rule for the negative charge, you place your palm perpendicular to the thumb, which now mimics the scenario where the positive charge would move.
This helps us discover that the magnetic field points into the page. Always use palm orientation to identify the magnetic field correctly.

• Thumb: direction opposite to movement
• Fingers: magnetic field direction
• Palm: force direction on a positive charge

This modified rule helps with consistent results for negative charge scenarios.

circular motion in magnetic fields

When a charged particle moves in a magnetic field, it often undergoes circular motion.
The particle's velocity direction continuously changes due to the magnetic force acting perpendicular to it.
For our example, a negative charge moves counterclockwise due to an inward magnetic field.

• The radius of the circle depends on the particle's speed, charge, and magnetic field strength.
• Fleming's left-hand rule for motion can also aid understanding.

This consistent perpendicular force results in circular motion in a plane, such as our case on paper. Understanding this concept is crucial for mastering particle dynamics in magnetic fields.