Question

A. State the Right-Hand Thumb Rule and describe how it helps determine the direction of magnetic field around a current-carrying conductor.
B. Explain how the magnetic field changes with distance from the conductor.

Hint:

Hold the wire in your right hand with the thumb along the current. For part B recall that the field of a straight wire is inversely proportional to distance.

Answer 1

Step 1: Understanding the Concept:
A straight wire carrying current produces a magnetic field around it. This field is not along the wire. It forms closed circles around the wire, in a plane at right angles to the wire.
The question asks two things. Part A asks for a rule that tells us which way these circles point. Part B asks how strong the field is as we move away from the wire.

Step 2: State the Right-Hand Thumb Rule (Part A):
Imagine holding the current-carrying straight conductor in your right hand. Keep the thumb stretched out along the wire.
The thumb must point in the direction of the conventional current. Then the curled fingers wrap around the wire.
The way the fingers curl gives the direction of the magnetic field lines around the conductor.

Step 3: How the rule gives the direction of the field:
Take a vertical wire with current going upward. Point the right thumb upward.
The fingers then curl anticlockwise when we look at the wire from above. So the field lines are anticlockwise circles around the wire.
If the current is reversed, the thumb points down. The fingers now curl clockwise, so the field direction also reverses.
So the rule lets us find the direction of the field at any point near the wire without doing an experiment.

Step 4: Variation of the field with distance (Part B):
The magnetic field around a long straight conductor at a distance \(r\) from it is given by
\[ B = \frac{\mu_0 I}{2\pi r} \]
Here \(I\) is the current and \(\mu_0\) is a constant. For a fixed current, this gives
\[ B \propto \frac{1}{r} \]
So the field is strongest very close to the wire. It becomes weaker as we move away, and it falls in inverse proportion to the distance.
If the distance is doubled, the field becomes half. In a diagram, the concentric circles are drawn farther apart as we move outward, which shows the weaker field.

Final Answer:
Part A: with the thumb of the right hand along the current, the curled fingers show the direction of the field lines. Part B: the field is inversely proportional to the distance, so it decreases as we move away from the conductor. \[ \boxed{B \propto \frac{1}{r}} \]