QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
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Problem 4.
A rectangular coil containing 20 loops (turns) is moving with a constant speed of $5.00 \mathrm{~cm} / \mathrm{s}$ toward a region containing a uniform magnetic field of 3.00 T pointing into the page. The dimensions of the coil are $a=$ 8.00 cm and $b= 12.0 \mathrm{~cm}$. The coil has a total resistance of $8.00 \Omega$.
(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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Step 1To solve this problem, we will analyze the induced electromotive force (emf) and current in the rectangular coil in different situations as it moves through a magnetic field.
### Step 1: Calculate the area of the coil The area 1$ - Magnetic flux: \Phi_B = 3.00 \, \text{T} \cdot 0.0072 \, \text{m}^2 = 0.0216 \, \text{Wb} - Rate of change of flux: - Induced emf: \mathcal{E} = - 0.012 \, \text{V} - Induced current: - Direction: By Lenz's law, the induced current will be clockwise. ### Step 4: Compare the situations In both situations where half the coil has entered the field and where 75% of the coil has exited the field, the induced emf is the same because the rate of change of the area exposed to the magnetic field is the same. The induced emf depends on the change in flux due to the area entering or exiting the magnetic field, which is proportional to the speed of the coil and the width of the coil. ###
Final Answer
(a) 1. Coil outside the field: $\mathcal{E} = 0 \, \text{V}, I = 0$. 2. Half the coil in the field: $\mathcal{E} = 0.012 \, \text{V}, I = 1.5 \, \text{mA}$ (counterclockwise). 3. Entirely in the field: $\mathcal{E} = 0 \, \text{V}, I = 0$. 4. 75% exited: $\mathcal{E} = 0.012 \, \text{V}, I = 1.5 \, \text{mA}$ (clockwise). (b) The induced emf is the same in both cases because the rate of change of magnetic flux is equal due to the same speed and width of the coil entering or exiting the magnetic field.
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