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Question Video: Calculating the Velocity of a Rod in a Magnetic Field Physics • 9th Grade

A rod with a length of 40 cm starts to slide on a track that makes an angle of 45° with a magnetic field of strength 0.3 T. If the induced emf at its terminals is measured to be 2.5 V, then the velocity of the rod is _. Give your answer to one decimal place.

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Video Transcript

Fill in the blank. A rod with a length of 40 centimeters starts to slide on a track that makes an angle of 45 degrees with a magnetic field of strength 0.3 teslas. If the induced emf at its terminals is measured to be 2.5 volts, then the velocity of the rod is blank. Give your answer to one decimal place. (A) 75.4 meters per second, (B) 29.5 meters per second, (C) 20.8 meters per second, or (D) 0.2 meters per second.

To begin answering this question, let’s draw a diagram so that we can visualize what’s happening. Now, we weren’t told a specific direction that the magnetic field points in. We can just choose to draw it pointing from left to right. Next, we were told that the rod is moving at a 45-degree angle to the magnetic field, so let’s add the rod to the sketch, along with an arrow to show its direction of motion.

At this point, we should recall the formula for the electromotive force, or emf, induced across the rod. For a straight conductor of length 𝑙, moving at a velocity 𝑣 through a magnetic field of strength 𝐵, with the velocity at an angle of 𝜃 relative to the field, the emf is given by 𝑙 times 𝑣 times 𝐵 times the sin of 𝜃. Here, 𝜃 equals 45 degrees.

In this question, we want to find the velocity of the rod. So let’s rearrange this equation to make 𝑣 the subject. To do this, we simply divide both sides of the equation by 𝑙, 𝐵, and sin 𝜃 to get 𝑣 by itself on one side of the equals sign. Thus, the expression can be written as 𝑣 equals the induced emf divided by 𝑙𝐵 sin 𝜃. Now, we already have values for all of the terms on the right-hand side of the equation, so next, we should make sure that all of them are expressed in the appropriate SI units.

The emf is given as 2.5 volts, so that’s good to go, and so is the strength of the magnetic field, written as 0.3 teslas. The only units that need to be converted here are centimeters for the length of the conducting rod, which should be in meters instead. We know that one centimeter is one hundredth of a meter, so let’s rewrite 40 centimeters as 0.40 meters.

With all the values on the right-hand side of this equation expressed in SI-derived units, we can be sure that this formula will give a final velocity value in SI-derived units of meters per second. So let’s go ahead and substitute all the values into the equation. And grabbing a calculator, we get a result of 29.4628 and so on meters per second. To one decimal place, our final answer becomes 29.5 meters per second, which corresponds to answer option (B). We have found that the rod moves at a velocity of 29.5 meters per second at an angle of 45 degrees to the magnetic field.

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