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Chapter 19: Problem 11

A uniform magnetic field points vertically upward; its magnitude is $0.800 \mathrm{T}\(. An electron with kinetic energy \)7.2 \times 10^{-18} \mathrm{J}$ is moving horizontally eastward in this field. What is the magnetic force acting on it?

Short Answer

Expert verified
Answer: To find the magnetic force, first, determine the electron's velocity using its kinetic energy, mass, and the equation \(v = \sqrt{\frac{2*KE}{m}}\). Then, calculate the magnetic force using the equation F = q(v x B), where F is the magnetic force, q is the charge of the electron, v is its velocity, and B is the magnetic field. After plugging in the values for q, v, and B and solving the expression, you will find the magnetic force acting on the electron.

Step by step solution

01

Find the electron's velocity

First, we will find the velocity of the electron using its kinetic energy and mass. The kinetic energy (KE) of the electron can be given by: KE = \(\frac{1}{2}mv^2\), where m is the mass of the electron and v is its velocity. Rearranging the equation for v, we get: v = \(\sqrt{\frac{2*KE}{m}}\) The mass of an electron (m) is approximately \(9.11 * 10^{-31} kg\) and the given kinetic energy (KE) is \(7.2 * 10^{-18} J\). Plugging these values into the equation, we can find the electron's velocity: v = \(\sqrt{\frac{2*(7.2*10^{-18})}{(9.11*10^{-31})}}\)
02

Calculate the magnetic force

The magnetic force acting on a charged particle is given by the following equation: F = q(v x B) Here, F is the magnetic force, q is the charge of the particle, v is its velocity, and B is the magnetic field. Since the electron is moving horizontally eastward in a vertically upward magnetic field, the angle between the velocity vector and magnetic field vector is 90 degrees. Therefore, the cross product (v x B) equals the product of v and B: v x B = v * B Now, we can plug in the values to find the magnetic force: F = (-1.6 * 10^{-19})(v)(0.800) (Note that the charge of an electron is negative, so we use -1.6 * 10^{-19} C for the charge.)
03

Compute the magnetic force

Now that we have found the electron's velocity and have the equation for magnetic force, we can plug in the values to compute the magnetic force acting on the electron: F = (-1.6 * 10^{-19})(v)(0.800) Using the value of v from Step 1, compute the final magnetic force acting on the electron: F = (-1.6 * 10^{-19})(\(\sqrt{\frac{2*(7.2*10^{-18})}{(9.11*10^{-31})}}\))(0.800) After evaluating this expression, the magnetic force acting on the electron can be determined.

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Most popular questions from this chapter

The strength of Earth's magnetic field, as measured on the surface, is approximately \(6.0 \times 10^{-5} \mathrm{T}\) at the poles and $3.0 \times 10^{-5} \mathrm{T}$ at the equator. Suppose an alien from outer space were at the North Pole with a single loop of wire of the same circumference as his space helmet. The diameter of his helmet is \(20.0 \mathrm{cm} .\) The space invader wishes to cancel Earth's magnetic field at his location. (a) What is the current required to produce a magnetic ficld (due to the current alone) at the center of his loop of the same size as that of Earth's field at the North Pole? (b) In what direction does the current circulate in the loop, CW or CCW, as viewed from above, if it is to cancel Earth's field?
An electron moves at speed \(8.0 \times 10^{5} \mathrm{m} / \mathrm{s}\) in a plane perpendicular to a cyclotron's magnetic field. The magnitude of the magnetic force on the electron is \(1.0 \times 10^{-13} \mathrm{N}\) What is the magnitude of the magnetic field?
A straight wire is aligned east-west in a region where Earth's magnetic field has magnitude \(0.48 \mathrm{mT}\) and direction \(72^{\circ}\) below the horizontal, with the horizontal component directed due north. The wire carries a current \(I\) toward the west. The magnetic force on the wire per unit length of wire has magnitude \(0.020 \mathrm{N} / \mathrm{m}\) (a) What is the direction of the magnetic force on the wire? (b) What is the current \(I ?\)
You want to build a cyclotron to accelerate protons to a speed of $3.0 \times 10^{7} \mathrm{m} / \mathrm{s} .$ The largest magnetic field strength you can attain is 1.5 T. What must be the minimum radius of the dees in your cyclotron? Show how your answer comes from Newton's second law.
The conversion between atomic mass units and kilograms is $$1 \mathrm{u}=1.66 \times 10^{-27} \mathrm{kg}$$ A sample containing carbon (atomic mass 12 u), oxygen \((16 \mathrm{u}),\) and an unknown element is placed in a mass spectrometer. The ions all have the same charge and are accelerated through the same potential difference before entering the magnetic field. The carbon and oxygen lines are separated by \(2.250 \mathrm{cm}\) on the photographic plate, and the unknown element makes a line between them that is \(1.160 \mathrm{cm}\) from the carbon line. (a) What is the mass of the unknown clement? (b) Identify the element.
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