Induced Potential
In this lesson we learn how changing current properties affects the induced potential.
IN THIS LESSON:
Changing current properties
Visualising their effects
Explaining current-time graphs
Click the image to enlarge it.
Practice Questions
Question 1: You push a magnet into a coil of wire. How does the speed at which you push the magnet affect the size of the induced potential?
Answer: If you move the magnet faster, you induce a larger potential difference.
Answer Walkthrough: The faster you move the magnet, the greater the rate at which the wire cuts the magnetic field lines, which induces a greater potential difference.
Question 2: How does using a stronger magnet affect the size of the induced potential?
Answer: Using a stronger magnet induces a larger potential difference.
Answer Walkthrough: A stronger magnet has more magnetic field lines. This means that for the same motion, more field lines are cut in the same amount of time, increasing the induced potential.
Question 3: A magnet is moved through a 50-turn coil and induces a potential of 0.2 V. If you replace it with a 100-turn coil and move the magnet at the same speed, what potential will be induced?
Answer: 0.4 V
Answer Walkthrough: The induced potential is directly proportional to the number of turns. Doubling the turns doubles the potential.
New potential = $0.2 \text{ V} \times (100/50) = 0.2 \text{ V} \times 2 = 0.4 \text{ V}$.
Question 4: You move a magnet into a coil and induce a current of 20 mA. What current is induced if you move the magnet at three times the speed?
Answer: 60 mA
Answer Walkthrough: The induced current is directly proportional to the speed of the motion. Tripling the speed triples the current.
New current = $20 \text{ mA} \times 3 = 60 \text{ mA}$.
Question 5: What is the effect of wrapping the coil around a soft iron core?
Answer: It increases the magnetic field strength inside the coil, which in turn increases the induced potential.
Answer Walkthrough: A soft iron core concentrates the magnetic field lines of the magnet, effectively making the field stronger.
Question 6: A magnet induces a potential of 0.5 V. You want to increase this to 1.5 V. If you keep the speed the same, by what factor must you increase the number of turns in the coil?
Answer: You must increase the number of turns by a factor of 3.
Answer Walkthrough: To triple the voltage (from 0.5 V to 1.5 V), you need to triple the number of turns.
Question 7: List three ways to increase the magnitude of the induced potential in a coil.
Answer:
- Move the magnet (or coil) faster.
- Use a stronger magnet.
- Use a coil with more turns.
- Wrap the coil around a soft iron core.
Question 8: A coil with 200 turns generates 1.2 V when a magnet is moved through it. What is the potential difference generated per turn of the coil?
Answer: 0.006 V per turn.
Answer Walkthrough:
Potential per turn = Total Potential / Number of turns = $1.2 \text{ V}/200 = 0.006 \text{ V}$.
Question 9: What two things can you change to reverse the direction of the induced current?
Answer:
- Reverse the direction of the magnet's motion (e.g., pull out instead of push in).
- Reverse the polarity of the magnet (e.g., use the South pole instead of the North pole).
Answer Walkthrough: Reversing the direction of the motion or the field will reverse the induced current.
Question 10: You push the North pole of a magnet into a coil, and the induced current flows in a clockwise direction. What happens to the direction of the current if you then pull the North pole straight back out?
Answer: The current will flow in the anti-clockwise (opposite) direction.
Answer Walkthrough: Reversing the direction of motion reverses the direction of the induced potential and current.
Question 11: You push the North pole into a coil, and the current flows clockwise. If you then push the South pole into the coil instead, what happens to the direction of the current?
Answer: The current will flow in the anti-clockwise (opposite) direction.
Answer Walkthrough: Reversing the polarity of the magnet is equivalent to reversing the direction of the magnetic field, which reverses the direction of the induced current.
Question 12: You push the North pole of a magnet into a coil. You then pull the South pole out of the coil. What is the final direction of the induced current compared to the original direction?
Answer: The current will flow in the same direction as the original.
Answer Walkthrough: You have reversed two things: the direction of motion (in to out) and the polarity of the magnet (North to South). The two reversals cancel each other out.
Question 13: In a bicycle dynamo, what is the best way for a cyclist to make the lights shine brighter without changing the dynamo itself?
Answer: The cyclist should pedal faster.
Answer Walkthrough: Pedalling faster makes the coil spin faster, increasing the speed at which it cuts magnetic field lines, which increases the induced potential and makes the light brighter.
Question 14: A magnet is dropped through a long coil of wire. How does the induced potential change in size as the magnet passes through?
Answer: The potential starts low, increases as the magnet accelerates due to gravity, and then decreases as it passes through the center and its speed relative to the coils outer parts might decrease. More accurately, the induced potential is maximum when the change in magnetic flux is greatest. This happens as the poles enter and leave the coil, and is zero when the magnet is fully inside and moving uniformly, or when it's at the very center where the field lines are most parallel to the coil's sides. Given the context of a falling magnet, its speed increases, so the magnitude of the induced potential will increase as it accelerates, reaching its peak when the change in flux is at its fastest (e.g., as the leading pole enters, and as the trailing pole exits). It will drop to zero when the magnet is fully within the coil and moving uniformly, or as it momentarily stops changing the flux linkage if it were to stop moving (which it doesn't, due to gravity). A more precise answer is that the potential will be non-zero as the magnet enters and leaves the coil, and its magnitude will increase as the magnet's speed increases due to gravity during these entry/exit phases.
Answer Walkthrough: As the magnet falls, its speed increases due to gravity. A greater speed means a greater rate of cutting field lines, so the induced potential gets bigger. The potential is zero when the magnet is fully inside the coil and moving uniformly, as there is no change in flux linkage in that region relative to the coil turns. It is maximum when the poles are entering or leaving the coil.
Question 15: True or False: A generator in a power station rotates its coil at a constant speed to produce a constant voltage.
Answer: False.
Answer Walkthrough: The generator produces an alternating potential difference (AC). The magnitude of the induced voltage changes as the coil rotates, being maximum when the coil is cutting the field lines at 90 degrees and zero when it is moving parallel to them. This produces a sinusoidal voltage output, which is not constant.