question 14 (1 point)
a coil lies flat on a horizontal table top in a region where the magnetic field points straight down. the magnetic field disappears suddenly. when viewed from above, what is the direction of the induced current in this coil as the field disappears?
○ counterclockwise
○ clockwise
○ clockwise initially, then counterclockwise before stopping
○ there is no induced current in this coil.

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# Brief Explanations:
To solve this, we use Lenz's Law, which states that the induced current will flow in a direction that opposes the change in magnetic flux. The magnetic field is pointing down and is decreasing (disappearing). The original magnetic flux is downward and decreasing. The induced magnetic field should oppose this decrease, so it should also point downward (to "replace" the decreasing field). Using the right - hand rule: if we curl the fingers of our right hand in the direction of the current, and the thumb points in the direction of the magnetic field (downward, in the case of the induced field), the fingers curl clockwise when viewed from above. Wait, no—wait, let's correct that. Wait, the original magnetic field is downward and is decreasing. The induced current's magnetic field should be in the same direction as the original (downward) to oppose the decrease (because the flux is decreasing, the induced field tries to maintain the flux). To get a downward - pointing magnetic field inside the coil (when viewed from above), using the right - hand grip rule: if the thumb points down (magnetic field direction), the fingers curl clockwise. Wait, no, actually, when you have a coil, the direction of the current and the magnetic field are related by the right - hand rule. Let's think again. The magnetic flux through the coil is $\Phi = B\cdot A$, with $B$ downward. As $B$ decreases, the change in flux $\Delta\Phi$ is negative (decreasing). By Faraday's law, the induced emf (and thus current) is such that the induced magnetic field $B_{ind}$ opposes $\Delta\Phi$. So $B_{ind}$ should be in the same direction as the original $B$ (downward) to oppose the decrease. Now, to find the direction of the current that produces a downward - pointing magnetic field inside the coil (viewed from above), we use the right - hand rule: curl the fingers of your right hand in the direction of the current, and your thumb points in the direction of the magnetic field inside the coil. If the thumb points down, the fingers curl clockwise. Wait, no, that's incorrect. Wait, when you look at the coil from above, and the magnetic field inside the coil is downward, the current direction is clockwise? Wait, no, let's take a simple example. If you have a current - carrying coil, and you look at it from above, a clockwise current produces a magnetic field that points downward (into the page), and a counter - clockwise current produces a magnetic field that points upward (out of the page). So in this case, the original magnetic field is downward and decreasing. The induced magnetic field should be downward (to oppose the decrease). So the current should be clockwise (because a clockwise current, viewed from above, produces a downward - pointing magnetic field inside the coil). Wait, but let's re - express Lenz's Law. The induced current will flow in a direction such that its magnetic field opposes the change in the original magnetic flux. The original flux is downward and decreasing. So the induced flux should be downward (to oppose the decrease). So the induced magnetic field is downward. Using the right - hand rule for the coil: when viewed from above, a clockwise current creates a magnetic field that points downward (into the table), and a counter - clockwise current creates a magnetic field that points upward (out of the table). So to get a downward - pointing induced magnetic field, the current must be clockwise? Wait, no, I think I messed up. Wait, the original magnetic field is downward (into the table). The flux is $B$ (downward) times area. As $B$ decreases, the flux decreases. The induced current's magnetic field should be in the same direction as the original (downward) to oppose the decrease (because the flux is decreasing, the induced field tries to "add" to the flux to keep it from decreasing). So the induced magnetic field is downward. So the current direction: when viewed from above, a clockwise current in the coil produces a magnetic field that is downward (into the coil). So the induced current is clockwise? Wait, no, wait, let's check with the right - hand rule again. Hold your right hand above the coil, fingers curled. If the current is clockwise (viewed from above), your fingers curl clockwise, and your thumb points downward (into the coil), which is the direction of the magnetic field. So yes, the induced current should be clockwise? Wait, no, I think I had it backwards earlier. Wait, no—wait, the original magnetic field is downward and is decreasing. The induced current's magnetic field should oppose the change. The change is a decrease in downward flux. So the induced magnetic field should be downward (to make up for the loss). So the current that produces a downward magnetic field inside the coil (viewed from above) is clockwise. Wait, but let's think of another way. Suppose the magnetic field is going into the page (downward) and is decreasing. The induced current will create a magnetic field that also goes into the page (to oppose the decrease). The right - hand rule for a coil: if the magnetic field is into the page (downward), the current is clockwise (when viewed from above). So the correct answer is clockwise? Wait, no, I think I made a mistake. Wait, let's use Lenz's Law properly. The flux is $\Phi = B A\cos	heta$, with $	heta = 0$ (since $B$ is perpendicular to the coil, which is flat on the table). The change in flux $\frac{d\Phi}{dt}=\frac{d(B A)}{dt}=A\frac{dB}{dt}$. Since $B$ is decreasing, $\frac{dB}{dt}<0$, so $\frac{d\Phi}{dt}<0$. The induced emf $\epsilon=-\frac{d\Phi}{dt}$, so $\epsilon>0$. The direction of the current is such that the magnetic field it produces opposes $\frac{d\Phi}{dt}$. So the induced magnetic field $B_{ind}$ should be in the same direction as $B$ (downward) to oppose the decrease. Now, to find the current direction: for a coil, the magnetic field inside is related to the current by the right - hand rule. If you want $B_{ind}$ downward (into the coil), the current is clockwise when viewed from above. Wait, no—wait, when you have a current - carrying loop, and you look at it from above, a clockwise current creates a magnetic field that points downward (into the loop), and a counter - clockwise current creates a magnetic field that points upward (out of the loop). So in this case, since we need $B_{ind}$ downward (into the loop) to oppose the decrease of the original downward $B$, the current should be clockwise. Wait, but I think I had a confusion earlier. Let's take a simple case: if the magnetic field is increasing downward, the induced current would be counter - clockwise (to produce an upward - pointing magnetic field to oppose the increase). But in our case, the magnetic field is decreasing downward, so the induced current should produce a downward - pointing magnetic field, which is clockwise. So the answer is clockwise.
# Answer:
B. clockwise

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