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Integrated Concepts (a) $\mathrm{A} 0.140-\mathrm{kg}$ baseball, pitched at 40.0 $\mathrm{m} / \mathrm{s}$ horizontally and perpendicular to the Earth's horizontal $5.00 \times 10^{-5} \mathrm{T}$ field, has a $100-\mathrm{nC}$ charge on it. What distance is it deflected from its path by the magnetic force, after traveling 30.0 $\mathrm{m}$ horizontally? (b) Would you suggest this as a secret technique for a pitcher to throw curve balls?

Part $(a) : 2.52 \mathrm{mm}$Part $(\mathrm{b}) : \mathrm{No}$

Physics 102 Electricity and Magnetism

Chapter 22

Magnetism

Magnetic Field and Magnetic Forces

Sources of Magnetic field

Electromagnetic Induction

Inductance

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so here for part A. We know that the radius of curvature, the bottom of the baseball, the baseball is gonna follow a curved path with a radius are equal in the mass. Times be divided by the charge times be and so here. This would be equal to the mass of the baseball 0.140 kilograms times the velocity of the baseball, 40 0.0 meters per second, divided by the charge on the baseball 100 nano cool arms which would simply be 100 times 10 to the negative ninth. Cool arms multiplied by B 5.0 times, 10 to the negative. Fifth Tesla's. This would be the essentially a magnetic field of earth. And so we find that the radius are is equal in 1.1 two times 10 to the 12th meters. This would be our This would just keep in mind this this radius because we know that this radius is very large. So the arc length can be approximated as the horizontal distance from the angle. Uh, who's on the distance? The artwork is equal to the horizontal distance. And so here we can say that the angle is approximately equal two That horizontal distance of 30.0 meters divided by 1.12 times 10 to the 12th meters and this would be multiplied by 360 degrees. And so this is gonna be equaling to a very small angle of 9.64 times 10 to the negative ninth degrees. And we can say that here, let's make a small figure where this single here would be stada, we would have our times. So we are here this distance here. This would be our 30.0 meters and then we have an angle here, Beta. Our angle here data the same thing. Uh, not drawn to scale, but this is what it would be. This is again data, and then this angle here would be considered Alfa. And so here, from the figure we can say that to beta plus data is equaling 180 degrees. That, of course, forms a triangle. And we know that beta plus alfa is equaling 90 degrees. And so we can say that two times 90 degrees minus Alfa plus veda is equaling. 180 degrees, 180 degrees minus two Alfa plus data equals 180 degrees. These cancel out and we have that Alfa is equaling Fada over too. And so Alfa is equaling the fate of that. We had just found 9.64 times 10 to the ninth. Other times 10 to the negative ninth degrees divided by two. This is equally 4.82 times 10 to the negative ninth degrees. And so from the figure, we can say that acts would be equally 30.0 meters time sign of Alfa and this would be equaling 30.0 meters times sign of 4.8 two times 10 to the negative ninth quantity degrees and we find that X is equaling 2.52 times 10 the negative ninth meters and so the distance deflected the distance that the baseball is deflected from its path due to the magnetic field of the earth is 2.52 times 10th of negative 90 meters. This would be our final answer for part a four part B. Now, however, this would not be helpful as the deflection is negligible. That is the end of the solution. Thank you for watching

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