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 1To 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$
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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