Lenz's Law Explained- Khan Academy Practice Problems
What Lenz's Law Actually Is
Lenz's Law states that the direction of an induced electric current is such that the magnetic field it creates opposes the change in magnetic flux that produced it. That's the textbook definition. Here's what that means in practice: when you change the magnetic field through a loop of wire, the induced current flows in a direction that tries to fight that change.
It's basically nature's way of saying "I don't like change." The induced magnetic field pushes back against whatever you're doing to alter the original field.
Why This Law Matters
Without Lenz's Law, you'd have no way to predict the direction of induced currents. Faraday's Law tells you the magnitude of the induced EMF, but it says nothing about which way the current flows. Lenz's Law fills that gap.
This law shows up everywhere:
- Electric generators
- Transformers
- Inductive heating systems
- Braking systems on trains
- Metal detectors
If it involves electromagnetic induction, Lenz's Law is in play.
Lenz's Law vs Faraday's Law
Students constantly confuse these two. Here's the difference:
| Law | What It Tells You | Formula |
|---|---|---|
| Faraday's Law | Magnitude of induced EMF | |ε| = N × dΦ/dt |
| Lenz's Law | Direction of induced current | Sign in Faraday's Law |
Faraday's Law gives you the size of the effect. Lenz's Law tells you which way the current goes. They're not competing—they're complementary.
The Right-Hand Rule Connection
To apply Lenz's Law, you need to use the right-hand rule correctly. Point your thumb in the direction of the induced magnetic field. Your fingers curl in the direction of current flow.
Here's the step-by-step process:
- Identify the direction of the external magnetic flux change
- Determine what the induced magnetic field should be (same direction if flux is decreasing, opposite if increasing)
- Apply the right-hand rule to find current direction
This three-step method works for almost every problem you'll encounter.
Khan Academy Practice Problems: What to Expect
Khan Academy's physics section includes solid practice problems on electromagnetic induction. The Lenz's Law problems typically fall into a few categories:
- Moving magnet problems — A magnet moves toward or away from a loop, you determine current direction
- Changing area problems — A loop expands or contracts within a magnetic field
- Changing field problems — The magnetic field strength increases or decreases through a stationary loop
The difficulty varies. Early problems give you labeled poles and directions. Later problems expect you to figure out everything from scratch.
How to Solve These Problems
Step 1: Analyze the Flux Change
Ask yourself: is the magnetic flux through the loop increasing or decreasing? Don't skip this step. Half of Lenz's Law problems come down to getting this wrong.
Step 2: Determine the Opposing Field
If flux is increasing, the induced field points opposite to the external field. If flux is decreasing, the induced field points in the same direction as the external field.
Step 3: Find the Current Direction
Use the right-hand rule. For a loop viewed from one side, clockwise current produces a field pointing away from you. Counterclockwise produces a field pointing toward you.
Step 4: Check Your Work
Verify that your induced current actually creates a magnetic field in the direction you determined in step 2. If it doesn't, something went wrong.
Common Mistakes on Khan Academy Problems
Confusing increasing and decreasing flux. This is the most common error. A magnet moving toward a loop increases flux. Moving away decreases it. Students often get this backwards.
Forgetting the right-hand rule. Some students memorize the clockwise/counterclockwise trick without understanding why it works. When problems flip the perspective or use different orientations, they get lost.
Ignoring the loop's orientation. The direction of induced current depends on which side of the loop you're viewing. A current that appears clockwise from one angle looks counterclockwise from the other side.
Skipping the "oppose the change" step. Students jump straight to the right-hand rule without first determining what the induced field should be. This leads to wrong directions almost every time.
Example Problem Walkthrough
Here's a typical Khan Academy setup: A north pole moves toward a circular loop. What direction does the induced current flow when viewed from the north side?
Solution:
- Flux is increasing (magnet getting closer, field strengthening)
- Induced field must point opposite to the external field (away from the approaching magnet)
- External field points toward the loop (north attracts south)
- Induced field must point away from the loop
- From the north side, a field pointing away requires counterclockwise current
The answer: counterclockwise when viewed from the north.
When Khan Academy Problems Get Tricky
Some problems involve multiple loops or changing loop shapes. The method stays the same:
- Calculate net flux through each loop separately
- Determine the induced EMF in each loop
- Apply Lenz's Law to each loop independently
- Add the effects if loops are connected
More loops means more math, but the physics doesn't change.
What Khan Academy Gets Right
The practice problems are well-designed. They start simple and build complexity gradually. The hints are actually helpful without giving away the entire solution. The videos explain the conceptual foundation before you hit the problems.
The feedback on wrong answers explains why you went wrong. That's worth more than most textbooks offer.
What to Do If You're Stuck
If a problem stumps you, watch the associated Khan Academy video first. The visual demonstrations make concepts click that reading cannot.
If you've watched the video and still struggle, identify the exact step where you get lost. Is it determining flux direction? Is it the right-hand rule? Is it connecting the induced field to current direction? Pinpoint the gap and focus there.
Working through five problems you understand is better than rushing through fifty you're guessing on.
The Bottom Line
Lenz's Law is straightforward: induced currents flow in directions that oppose the changes causing them. The math is simple. The conceptual application trips people up.
Master the flux-change-first approach. Practice the right-hand rule until it's automatic. Work through Khan Academy's problem sets in order. You'll get it.