Explain Electromagnetic Induction - Physics

1. A coil has $N=200$ and flux per turn changes at $\frac{d\Phi}{dt}=0.01\ \text{Wb s}^{-1}$. Find $|\varepsilon|$.

   $2\ \text{V}$. $|\varepsilon| = N|\frac{d\Phi}{dt}| = 200 \times 0.01 = 2\ \text{V}$.

2. What is the direction rule for induced current when the magnetic flux increases?

   The induced field opposes the increase in flux. Lenz's law: induced current creates field opposing flux increase.

3. Identify the meaning of the minus sign in $\varepsilon=-N\frac{\Delta\Phi}{\Delta t}$.

   Lenz's law: induced emf opposes the flux change. Induced effects always oppose their cause.

4. What experimental observation shows that faster motion induces a larger emf?

   Greater galvanometer deflection at higher speed. Faster flux change produces larger $|\varepsilon|$ by Faraday's law.

5. A loop moves into a region of stronger $B$. What is the sign of $\frac{d\Phi}{dt}$?

   $\frac{d\Phi}{dt}>0$. Flux increases as loop enters stronger field region.

6. A coil is moved out of a uniform magnetic field region. What must be true for induction?

   The flux through the coil must change. Leaving field changes flux from $BA$ to zero.

7. A north pole moves away from a coil. Which pole is induced on the near face of the coil?

   The near face becomes a south pole. Unlike poles attract to oppose separation.

8. A magnet is moved toward a coil faster. How does induced emf magnitude change?

   It increases because $\left|\frac{\Delta\Phi}{\Delta t}\right|$ increases. Faster motion gives larger flux change rate.

9. What is the direction rule for induced current when the magnetic flux decreases?

   The induced field opposes the decrease in flux. Lenz's law: induced current tries to maintain original flux.

10. What evidence shows induced current depends on relative motion between magnet and coil?

    Moving the coil instead of the magnet gives the same deflection. Either motion produces same flux change.

11. State Faraday's law in symbols for a coil with $N$ turns.

    $\varepsilon=-N\frac{\Delta\Phi}{\Delta t}$. Induced emf equals turns times rate of flux change.

12. A coil rotates so $\theta$ increases from $0^\circ$ to $90^\circ$. What happens to $\Phi$?

    It decreases from $BA$ to $0$. $\cos(90°) = 0$, so flux becomes zero.

13. Which change is necessary to induce an emf in a stationary closed loop?

    A change in magnetic flux through the loop. Faraday's law requires $\frac{d\Phi}{dt} \neq 0$.

14. Which change increases magnetic flux $\Phi$ through a fixed coil: increasing $B$, $A$, or $\cos\theta$?

    Any increase in $B$, $A$, or $\cos\theta$ increases $\Phi$. All three factors multiply to give flux.

15. What happens to induced emf if the number of turns $N$ in a coil is doubled?

    It doubles, since $\varepsilon\propto N$. Faraday's law shows emf is directly proportional to turn count.

16. A transformer works by induction. What must be true about current in the primary coil?

    It must be changing (typically alternating). AC creates changing flux in the core.

17. What happens to induced emf if the number of turns doubles, with the same $\frac{\Delta\Phi}{\Delta t}$?

    It doubles: $\varepsilon\propto N$. Faraday's law shows emf is directly proportional to $N$.

18. Use Faraday's law: if $\Delta\Phi=0.020\,\text{Wb}$ in $0.10\,\text{s}$ for $N=50$, find $|\varepsilon|$.

    $|\varepsilon|=10\,\text{V}$. $|\varepsilon| = 50 \times \frac{0.020}{0.10} = 10\,\text{V}$

19. What is the induced current direction rule that opposes the change in flux called?

    Lenz's law. States induced current opposes flux change.

20. A loop has $A=0.30\ \text{m}^2$, $B=0.40\ \text{T}$, and $\theta=90^\circ$. What is $\Phi$?

    $0\ \text{Wb}$. $\cos(90°) = 0$, so flux is zero when $\vec{B} \perp$ area normal.

21. A loop moves out of a magnetic field region so flux decreases. What is the sign of $\frac{d\Phi}{dt}$?

    $\frac{d\Phi}{dt}<0$. Flux decreases as loop exits field region.

22. What experimental observation shows that reversing motion reverses induced current?

    Galvanometer deflection reverses when motion direction reverses. Reversing $\frac{d\Phi}{dt}$ sign reverses induced current direction.

23. What does magnetic flux $\Phi$ equal for a uniform field through area $A$?

    $\Phi=BA\cos\theta$. Flux is field times area times cosine of angle between them.

24. A rod moves parallel to magnetic field lines. What is the motional emf?

    $\varepsilon=0$. No flux cut when motion is along field lines.

25. Identify the condition that produces zero induced emf in a loop.

    $\frac{d\Phi}{dt}=0$. No flux change means no induced emf by Faraday's law.

26. A north pole approaches a coil. Which face of the coil becomes a north pole?

    The near face becomes a north pole. Like poles repel to oppose approach.

27. What evidence shows that induced current creates its own magnetic field?

    It produces a force opposing motion or a measurable magnetic effect. Induced currents create observable magnetic forces and fields.

28. What condition must occur for an emf to be induced in a conductor or coil?

    A changing magnetic flux linkage through it. Faraday's law requires flux change for induction.

29. A loop has $A=0.50\ \text{m}^2$, $B=0.20\ \text{T}$, and $\theta=0^\circ$. What is $\Phi$?

    $0.10\ \text{Wb}$. $\Phi = BA\cos(0°) = 0.20 \times 0.50 \times 1 = 0.10\ \text{Wb}$.

30. Which observation is direct evidence of electromagnetic induction in a coil?

    A galvanometer deflects only while flux is changing. No deflection when flux is constant proves change is needed.

31. What does the minus sign in Faraday's law represent?

    Lenz's law: induced emf opposes the change in magnetic flux. Induced current creates field opposing the flux change.

32. What experimental observation shows that reversing magnet polarity reverses induced current?

    Galvanometer deflection reverses when the magnet is flipped. Flipping magnet reverses $\vec{B}$ direction and flux change sign.

33. If a magnet is held stationary inside a coil, what is the induced emf?

    $\varepsilon=0$. No flux change means no induced emf by Faraday's law.

34. State the formula for motional emf for a rod of length $\ell$ moving at speed $v$ in field $B$.

    $\varepsilon=B\ell v$. Derived from Faraday's law for moving conductor.

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