QQuestionPhysics
QuestionPhysics
Problem 4. a b XXXXXXXXX XXXXXXXXX XXXXXXXXX XXXXXXXXX XXXXXXXXX XXXXXXXXX A rectangular coil containing 20 loops (turns) is moving with a constant speed of 5.00 cm/s toward a region containing a uniform magnetic field of 3.00T pointing into the page. The dimensions of the coil are
8.00 cm and
cm. The coil has a total resistance of 8.00
. (a) Consider four different situations: the coil is completely outside the field, half the coil has entered the field, the coil is entirely within the field, 75% of the coil has exited the field. In each of the four situations, determine the induced emf and induced current in the coil. If the current is non-zero, use Lenz's law to determine if it is clockwise or counterclockwise. (b) Compare the situation when half the coil has entered the field to the one when only 25% of it has entered the field. Explain why the induced emf is the same in both cases.
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Answer
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Step 1:To solve this problem, we will break it down into two parts: (a) calculating the induced electromotive force (emf) and current for each situation, and (b) comparing the situations when half the coil has entered the magnetic field and when only 25% of it has entered.
\mathcal{E} = -N B \cdot \frac{dA}{dt} = -N B w v
### Given Data: - Number of loops (turns), 1$ is the magnetic flux given by: The area entering the field per unit time is: Thus, the induced emf becomes: ### Step 3: Analyze each situation
Step 2:**Completely outside the field**:
- 1$
Step 3:**Half the coil has entered the field**:
- Current \( I = \frac{\mathcal{E}}{R} = \frac{0.24}{8.00} = 0.030 \, \text{A} \)
- Change in area per unit time is 1$ - Induced emf: - Direction: Counterclockwise (using Lenz's law).
Step 4:**Entirely within the field**:
- Current \( I = \frac{0.48}{8.00} = 0.060 \, \text{A} \)
- Area 1$ - Induced emf: - Direction: Counterclockwise.
Step 5:** 75% of the coil has exited the field**:
- Current \( I = \frac{0.24}{8.00} = 0.030 \, \text{A} \)
- Area 1$ ### Explanation The induced emf is different in these two cases because the area entering the magnetic field is different. When half the coil is entering, the rate of change of magnetic flux is higher than when only 25% is entering. ###
Final Answer
(a) - Completely outside: 1$ (Clockwise) (b) The induced emf is the same when half the coil has entered the field and when only 25% has entered because the rate of change of magnetic flux is the same in both cases.
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