Question

Imagine that you are sitting in a chamber with your back to one wall. An electron beam, moving horizontally towards the front wall from the back wall, is deflected by a strong magnetic field to your right side. Find the direction of the magnetic field.

Hint:

For electron beam: Current direction is opposite to electron flow. Use Fleming's Left Hand Rule with current direction = opposite to electron motion. Force on electron = to right \(\Rightarrow\) magnetic field upward.

Answer 1

Step 1: Understand the given situation.

• You are sitting in a chamber with your back to one wall.
• An electron beam is moving horizontally from the back wall towards the front wall (i.e., from behind you to in front of you).
• The beam is deflected to your right side.
• We need to find the direction of the magnetic field.

Step 2: Establish coordinate system.
Let's define directions from your perspective:

• Front wall = direction you are facing
• Back wall = behind you
• Right side = your right hand side
• Left side = your left hand side

So:

• Electron beam direction: from back to front = forward direction (let's call this +x direction)
• Deflection direction: to your right = +y direction

Step 3: Important note about electron beam.
Electrons are negatively charged. The direction of conventional current is opposite to the direction of electron flow. Electron flow = forward (+x direction) Therefore, conventional current direction = backward (-x direction)
Step 4: Apply Fleming's Left Hand Rule.
Fleming's Left Hand Rule is used for the direction of force on a current-carrying conductor in a magnetic field. It states:

• Forefinger \(\Rightarrow\) direction of magnetic field (B)
• Middle finger \(\Rightarrow\) direction of current (I)
• Thumb \(\Rightarrow\) direction of force (F)

Step 5: Determine known directions.

• Force (deflection) direction = right side (+y direction)
• Current direction = opposite to electron flow = backward (-x direction)

Step 6: Find magnetic field direction.
Using Fleming's Left Hand Rule:

• Point your middle finger in the direction of current (backward, i.e., away from front wall)
• Point your thumb in the direction of force (right side)
• Your forefinger will then point in the direction of magnetic field

When you do this, your forefinger points upward (towards the ceiling).
Step 7: Verify with right-hand rule for negative charges.
For electrons (negative charges), we can also use Fleming's Right Hand Rule or the Left Hand Rule with reversed current. The result is the same: magnetic field is upward.
Step 8: Final answer.
\[ \boxed{\text{The magnetic field direction is vertically upward (towards the ceiling).}} \]