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Chapter 19: Problem 22

The magnetic field in a cyclotron is \(0.50 \mathrm{T}\). Find the magnitude of the magnetic force on a proton with speed $1.0 \times 10^{7} \mathrm{m} / \mathrm{s}$ moving in a plane perpendicular to the field.

Short Answer

Expert verified
Answer: The magnitude of the magnetic force on the proton is \(8.0 \times 10^{-19} \mathrm{N}\).

Step by step solution

01

Identify the given quantities and the required formula

We are given that: Magnetic field, B = 0.50 T Speed of the proton, v = \(1.0 \times 10^7 \mathrm{m/s}\) Charge of a proton, q = \(1.6 \times 10^{-19} \mathrm{C}\) The angle between the magnetic field and the velocity, θ = 90° (perpendicular) We need to find the magnetic force, F, which can be calculated using the formula: \(F = qvB\sin\theta\)
02

Calculate the sine of the angle

Since the angle between the magnetic field and the velocity is 90° (perpendicular), the sine function is as follows: \(\sin\theta = \sin 90° = 1\)
03

Calculate the magnetic force

Now we can plug in the given values and the sine function into the formula for F: \(F = qvB\sin\theta = (1.6 \times 10^{-19}\mathrm{C})(1.0 \times 10^7 \mathrm{m/s})(0.50 \mathrm{T})(1)\) Multiplying the given values, we get: \(F = 8.0 \times 10^{-19} \mathrm{N}\) Therefore, the magnitude of the magnetic force on the proton is \(8.0 \times 10^{-19} \mathrm{N}\).

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Most popular questions from this chapter

At a certain point on Earth's surface in the southern hemisphere, the magnetic field has a magnitude of \(5.0 \times 10^{-5} \mathrm{T}\) and points upward and toward the north at an angle of \(55^{\circ}\) above the horizontal. A cosmic ray muon with the same charge as an electron and a mass of $1.9 \times 10^{-28} \mathrm{kg}$ is moving directly down toward Earth's surface with a speed of \(4.5 \times 10^{7} \mathrm{m} / \mathrm{s} .\) What is the magnitude and direction of the force on the muon?
The magnetic field in a cyclotron is \(0.360 \mathrm{T}\). The dees have radius \(82.0 \mathrm{cm} .\) What maximum speed can a proton achicve in this cyclotron?
A solenoid of length \(0.256 \mathrm{m}\) and radius \(2.0 \mathrm{cm}\) has 244 turns of wire. What is the magnitude of the magnetic field well inside the solenoid when there is a current of \(4.5 \mathrm{A}\) in the wire?
(a) A proton moves with uniform circular motion in a magnetic field of magnitude 0.80 T. At what frequency \(f\) does it circulate? (b) Repeat for an electron.
An electromagnetic flowmeter is used to measure blood flow rates during surgery. Blood containing Na" ions flows due south through an artery with a diameter of \(0.40 \mathrm{cm} .\) The artery is in a downward magnetic field of \(0.25 \mathrm{T}\) and develops a Hall voltage of \(0.35 \mathrm{mV}\) across its diameter. (a) What is the blood specd (in \(\mathrm{m} / \mathrm{s}\) )? (b) What is the flow rate (in \(\mathrm{m}^{3} / \mathrm{s}\) )? (c) The leads of a voltmeter are attached to diametrically opposed points on the artery to measure the Hall voltage. Which of the two leads is at the higher potential?
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