e. explain your use of a hand rule to determine if the magnet is pulled up through the solenoid or pushed down through the solenoid and determine the induced magnetic poles of the solenoid. (2 marks)

Question

Accepted Answer

# Brief Explanations:
1. **Lenz's Law & Hand Rule (Right-Hand Grip Rule)**: First, recall Lenz's Law (induced current opposes the change in magnetic flux). The magnetic field direction inside the solenoid (from the diagram's arrows) is upward (toward the top of the solenoid). Using the Right-Hand Grip Rule: curl fingers in current direction, thumb points to induced magnetic pole.
2. **Determine Motion & Poles**: The induced magnetic field inside the solenoid (from current) must oppose the magnet's motion. The magnet’s south pole is near the solenoid. If the solenoid’s top pole is N, it would repel the magnet (pushing it down) or attract? Wait, no—wait, the magnetic field inside the solenoid (arrows) is upward, so thumb (Right-Hand Grip) points up, meaning the top of the solenoid is a **N pole** (since thumb is north pole direction). Now, Lenz’s Law: the induced current creates a field opposing the magnet’s motion. The magnet’s S pole is near the solenoid’s top (N pole)? Wait, no—wait, the magnet is above the solenoid: N at top, S at bottom (near solenoid’s top). Wait, the solenoid’s top pole: if the induced field inside is upward (arrows), then top of solenoid is N (since magnetic field lines exit N, enter S). Now, the magnet’s S pole is near the solenoid’s N pole? Wait, no—opposite poles attract, like poles repel. Wait, maybe the magnet is being pulled up or pushed down? Wait, the induced current’s magnetic field: if the solenoid’s top is N, and the magnet’s bottom is S, then N and S attract. But Lenz’s Law says the induced field opposes the change. Wait, maybe the magnet is moving down (pushed down) or up? Wait, no—let’s re-express:

Right-Hand Grip Rule: For the solenoid, fingers curl in current direction, thumb is magnetic field direction (inside solenoid). The diagram shows arrows inside solenoid pointing up, so thumb points up → top of solenoid is N pole.

Now, Lenz’s Law: the induced current opposes the magnet’s motion. The magnet has N (top) and S (bottom, near solenoid). If the solenoid’s top is N, then the magnet’s S (bottom) and solenoid’s N (top) attract. But if the magnet were moving down (toward solenoid), the induced field would oppose that (repel), but here they attract. Wait, maybe the magnet is being pulled up? No—wait, maybe I got the direction wrong. Wait, the magnetic field inside the solenoid is upward (arrows), so the top of the solenoid is N, bottom is S. The magnet’s S is near the solenoid’s N: opposite poles attract, so the solenoid would pull the magnet down (pushed down) or up? Wait, no—if the solenoid’s top is N, and the magnet’s bottom is S, they attract, so the solenoid would pull the magnet down (toward it), meaning the magnet is being pushed down? Wait, no—“pulled up” or “pushed down”: if the solenoid attracts the magnet, the magnet is pulled down (toward solenoid) or pushed up? Wait, no—if the solenoid’s top is N and magnet’s bottom is S, attraction means the solenoid pulls the magnet down (so magnet is pushed down through the solenoid? Wait, no—the magnet is above the solenoid, so “pulled up” would be away, “pushed down” toward. Wait, maybe I messed up the pole direction. Wait, magnetic field inside solenoid: arrows point up, so field lines go from bottom (S) to top (N) inside? No—magnetic field lines go from N to S outside, S to N inside. Wait, no: inside a solenoid, the magnetic field is uniform and directed from S pole to N pole (inside the solenoid). Wait, no—wait, a bar magnet: N pole, field lines exit N, enter S. Inside the magnet, field lines go S to N. For a solenoid, the magnetic field inside is like a bar magnet: field lines go from S (bottom of solenoid) to N (top of solenoid) inside. So outside, field lines go from N (top) to S (bottom). So the top of the solenoid is N, bottom is S. Now, the magnet above: N (top), S (bottom, near solenoid’s top, which is N). Wait, N and N repel? Wait, no—solenoid’s top is N, magnet’s bottom is S: N and S attract. Wait, I think I confused the pole. Wait, no—magnetic field inside solenoid is upward (arrows), so the top of the solenoid is N (because field lines exit N, enter S; inside, they go S to N). So inside solenoid: S (bottom) → N (top). So outside, field lines go N (top) → S (bottom). So the top of the solenoid is N, bottom is S. Now, the magnet’s bottom is S (near solenoid’s top, N). So N and S attract: the solenoid’s N (top) attracts the magnet’s S (bottom), so the magnet is pulled down (pushed down) through the solenoid? Wait, no—the magnet is above the solenoid, so “pushed down” would be toward the solenoid, “pulled up” away. Wait, attraction means the solenoid pulls the magnet down (toward it), so the magnet is pushed down (or pulled down) through the solenoid? Wait, maybe the key is: using Right-Hand Grip to find the solenoid’s poles (top N), then Lenz’s Law: the induced current opposes the magnet’s motion. If the magnet were moving down (toward solenoid), the induced field would repel it (oppose), but here they attract, so maybe the magnet is moving up (being pulled up), and the induced field attracts it to oppose the upward motion? Wait, no—Lenz’s Law: the induced effect opposes the cause (change in flux). If the magnet is moving up (away from solenoid), the flux through solenoid decreases (since magnet’s field is downward? Wait, no—the magnet’s field: N at top, S at bottom, so magnetic field lines go from N to S, so below the magnet (near solenoid), the field is downward (toward S pole). Wait, maybe I got the magnetic field direction wrong. Let’s start over:

1. **Magnetic Field of Magnet**: The bar magnet has N (top) and S (bottom). The magnetic field lines around the magnet go from N to S, so near the solenoid (below the magnet), the magnetic field lines are directed downward (toward the magnet’s S pole).

2. **Change in Flux**: If the magnet is moving down (toward solenoid), the flux through solenoid (downward) increases. If moving up, flux decreases.

3. **Induced Field (Lenz’s Law)**: Opposes the change. So if flux is increasing (magnet moving down), induced field is upward (opposite to downward flux). If flux is decreasing (magnet moving up), induced field is downward (same as original flux, to oppose decrease).

4. **Right-Hand Grip for Solenoid**: The diagram shows arrows inside solenoid pointing up, so induced field is upward. Therefore, the change in flux is a **decrease** (since induced field opposes decrease by adding same direction? Wait, no—Lenz’s Law: induced field opposes the change. So if original flux is downward (from magnet) and decreasing (magnet moving up), induced field is downward (to oppose the decrease, i.e., maintain flux). Wait, no—this is confusing. Wait, the diagram’s solenoid has arrows pointing up, so induced field is upward. Therefore, original flux (from magnet) must be downward, and the change is a **decrease** (so induced field is upward to oppose the decrease). Therefore, the magnet is moving **up** (pulled up), causing flux (downward) to decrease, so induced field is upward (opposes the decrease by creating upward field).

Now, solenoid’s poles: induced field inside is upward, so top of solenoid is N (Right-Hand Grip: thumb up, top is N).

So summarizing:
- Use **Right-Hand Grip Rule** to find solenoid’s poles: fingers curl in current direction (from diagram’s arrows and galvanometer), thumb points up → top of solenoid is N pole.
- Use **Lenz’s Law**: induced field (upward) opposes the change in flux. Original flux (from magnet) is downward (since magnet’s S is near solenoid, field lines toward S). If magnet moves up, flux (downward) decreases → induced field (upward) opposes this decrease (by creating upward field). Thus, magnet is **pulled up** through the solenoid.
- Induced magnetic poles: top of solenoid is N, bottom is S (since field inside is upward, from S to N inside, so top is N, bottom is S).

Wait, but the question says “determine if the magnet is pulled up through the solenoid or pushed down” and “induced magnetic poles”. Let’s confirm:

- Right-Hand Grip: Arrows inside solenoid are upward → thumb (N pole) points up → top of solenoid is N.
- Lenz’s Law: The induced field (upward) opposes the change. The magnet’s field near solenoid is downward (toward S pole). If magnet moves up, downward flux decreases → induced field (upward) opposes this (tries to keep flux same) → so magnet is pulled up (moving away, flux decreasing).
- Induced poles: top N, bottom S.

So the explanation: Use the Right-Hand Grip Rule: curl right hand fingers in the direction of induced current (from galvanometer), thumb points to the induced magnetic field direction (upward inside solenoid), so top of solenoid is N pole. By Lenz’s Law, the induced field opposes the magnet’s motion: the magnet’s S pole is near the solenoid’s N pole? Wait, no—wait, the magnet’s field near solenoid is downward (toward S), so when magnet moves up, downward flux decreases, induced field is upward (opposes decrease). Thus, magnet is pulled up, and solenoid’s top is N, bottom is S.

# Brief Explanations:
1. **Right-Hand Grip Rule**: Curl right hand fingers with the induced current (from galvanometer), thumb points upward (matches solenoid’s internal field arrows), so the solenoid’s **top is a N pole** (bottom is S).
2. **Lenz’s Law**: The induced magnetic field (upward) opposes the change in flux. The bar magnet’s magnetic field near the solenoid is downward (toward its S pole). If the magnet moves **up** (pulled up), the downward flux through the solenoid decreases. The induced upward field opposes this decrease (by “replacing” lost flux), confirming the magnet is pulled up.
3. **Induced Poles**: Top of solenoid = N (field exits N), bottom = S (field enters S).

# Answer:
The magnet is pulled up through the solenoid. The induced magnetic pole at the top of the solenoid is a North (N) pole, and the bottom is a South (S) pole. Explanation: Using the Right-Hand Grip Rule, the upward internal field (arrows) means the top of the solenoid is N. By Lenz’s Law, the induced field (upward) opposes the decreasing downward flux (from the magnet moving up), so the magnet is pulled up. The solenoid’s top is N, bottom is S.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Answer: