00 Practice On Right Hand Rule and Flemings Left Hand Rule | PDF - Free Printable

To solve this problem, we need to determine the direction of the magnetic force on a current-carrying conductor placed in a uniform magnetic field. The force is given by the formula:

$$
\vec{F} = I(\vec{L} \times \vec{B})
$$

Where:
- $ I $ is the current,
- $ \vec{L} $ is the length vector of the wire (in the direction of current),
- $ \vec{B} $ is the magnetic field vector,
- $ \times $ denotes the cross product.

The direction of the force is determined using either:
- Fleming’s Left-Hand Rule, or
- The Right-Hand Rule for cross products.

We'll use Fleming’s Left-Hand Rule (for motors), which states:
- Thumb → Direction of Force ($ F $)
- Index finger → Direction of Magnetic Field ($ B $)
- Middle finger → Direction of Current ($ I $)

All three are mutually perpendicular.

Let’s go through each case one by one.

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(a)

- Magnetic field $ \vec{B} $: Into the page (indicated by ×)
- Current $ I $: To the right (→)

Using Fleming’s left-hand rule:
- Point index finger into the page (×) → toward you (but since it's ×, it's into the page).
- So, index finger points into the page.
- Middle finger points to the right (direction of current).
- Now, thumb gives the force direction.

Now, imagine:
- Index finger: into the page (away from you)
- Middle finger: to the right
- Then thumb will point downward.

✔ Force direction: Downward (↓)

---

(b)

- $ \vec{B} $: Into the page (×)
- $ I $: Upward (↑)

Fleming’s left-hand rule:
- Index finger: into the page
- Middle finger: upward
- Thumb: now points to the left

✔ Force direction: Left (←)

---

(c)

- $ \vec{B} $: Leftward (←)
- $ I $: Upward (↑)

Fleming’s left-hand rule:
- Index finger: to the left
- Middle finger: upward
- Thumb: points out of the page (toward you)

In diagrams, out of the page is represented by • (dot).

✔ Force direction: Out of the page (•)

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(d)

- $ \vec{B} $: Out of the page (•)
- $ I $: To the right (→)

Fleming’s left-hand rule:
- Index finger: out of the page (toward you)
- Middle finger: to the right
- Thumb: points upward

✔ Force direction: Upward (↑)

---

(e)

- $ \vec{B} $: Upward (↑)
- $ I $: Downward (↓)

Note: Current is downward, so $ \vec{L} $ is downward.

Fleming’s left-hand rule:
- Index finger: upward (B)
- Middle finger: downward (I)
- But wait — middle finger must be in direction of current, so point it down.
- Now, index finger up, middle finger down → they are opposite, but still perpendicular to thumb.

Now, cross product: $ \vec{L} \times \vec{B} $

But $ \vec{L} $ is downward, $ \vec{B} $ is upward → both are parallel, but opposite → angle = 180°

So $ \vec{F} = I(\vec{L} \times \vec{B}) = I(LB \sin 180^\circ) = 0 $

Because $ \sin 180^\circ = 0 $

So, no force when current and magnetic field are anti-parallel.

✔ Force direction: Zero (no force)

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(f)

- $ \vec{B} $: Downward (↓)
- $ I $: To the left (←)

Fleming’s left-hand rule:
- Index finger: downward (B)
- Middle finger: to the left (I)
- Thumb: points into the page (×)

✔ Force direction: Into the page (×)

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✔ Final Answers:

| Part | Magnetic Force Direction |
|------|--------------------------|
| (a) | Downward (↓) |
| (b) | Left (←) |
| (c) | Out of the page (•) |
| (d) | Upward (↑) |
| (e) | Zero (no force) |
| (f) | Into the page (×) |

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🔍 Summary Explanation:

- Use Fleming’s Left-Hand Rule:
- Index → $ \vec{B} $
- Middle → $ \vec{I} $
- Thumb → $ \vec{F} $
- If $ \vec{B} $ and $ \vec{I} $ are parallel or anti-parallel, force is zero.
- Cross product direction follows right-hand rule, but Fleming’s left-hand rule is easier for motor-type problems.

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