Question
For a person standing at midpoint O, the direction of current in loop A is clockwise and in loop B it is also clockwise. The magnitude of current in each loop is shown in the figure. Determine the direction of the net magnetic field at point O.
Solution
Step 1: Identify the observer
The observer is located at the midpoint O between the two circular current loops.
Step 2: Apply Right-Hand Thumb Rule for Loop A
- Looking towards Loop A, the current appears clockwise.
- For a clockwise current, magnetic field is directed away from the observer.
- Hence, magnetic field due to Loop A (BA) points towards Loop A.
Step 3: Apply Right-Hand Thumb Rule for Loop B
- Looking towards Loop B, current is also clockwise.
- Therefore magnetic field is again directed away from the observer.
- Hence, magnetic field due to Loop B (BB) points towards Loop B.
Step 4: Compare Magnitudes
Point O lies exactly at the midpoint of both loops.
- Distance from O to both loops is identical.
- Radius of both loops is equal.
- Magnetic field at equal distance is directly proportional to current.
| Loop | Current | Magnetic Field |
|---|---|---|
| A | i | BA |
| B | 4i | BB |
Therefore,
Step 5: Net Magnetic Field
Since the magnetic fields are along the same line but in opposite directions, the resultant magnetic field is
Because BB > BA, the net magnetic field points towards Loop B.
✅ Final Answer:
The net magnetic field at point O is directed towards Loop B.
đź’ˇ Key Concepts Used
- Right-Hand Thumb Rule
- Magnetic Field due to Circular Current Loop
- Direction of Magnetic Field
- Superposition Principle of Magnetic Fields
- Magnetic field is directly proportional to current (B ∝ I)
🎯 JEE Main Exam Tip
Whenever two current loops produce magnetic fields at the same point:
- ✔ First determine the direction using the Right-Hand Thumb Rule.
- ✔ Then compare magnitudes using B ∝ I (if radius and distance are same).
- ✔ Finally apply vector addition (superposition principle).