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Chapter 19: Problem 9

Find the magnetic force exerted on a proton moving east at a speed of $6.0 \times 10^{6} \mathrm{m} / \mathrm{s}\( by a horizontal magnetic ficld of \)2.50 \mathrm{T}$ directed north.

Short Answer

Expert verified
Answer: The magnetic force exerted on the proton is \(2.40 \times 10^{-12} \, N\).

Step by step solution

01

Identify relevant information and formula

We are given the following information: - The velocity of the proton, \(v = 6.0 \times 10^6 \frac{m}{s}\) (eastward) - The magnetic field, \(B = 2.50 \, T\) (northward) - Charge of a proton, \(q = 1.6 \times 10^{-19} \, C\) We will use the formula for the magnetic force on a moving charged particle: \(F = q|\vec{v}||\vec{B}|\sin{\theta}\), where \(\theta\) is the angle between the velocity and magnetic field vectors. In this problem, the proton is moving eastward while the magnetic field is directed northward, which means that the angle between the two is \(\theta = 90^{\circ}\).
02

Calculate the magnetic force

Now plug in the values given into the force equation: \(F = (1.6 \times 10^{-19} \, C)(6.0 \times 10^6 \frac{m}{s})(2.50 \, T)\sin{90^{\circ}}\) Since \(\sin{90^{\circ}} = 1\), the formula simplifies to: \(F = 1.6 \times 10^{-19} \, C \times 6.0 \times 10^6 \frac{m}{s} \times 2.50 \, T\) Multiplying these values gives us the magnetic force exerted on the proton: \(F = 2.40 \times 10^{-12} \, N\)
03

State the final answer

The magnetic force exerted on a proton moving east at a speed of \(6.0 \times 10^6 \frac{m}{s}\) by a horizontal magnetic field of \(2.50 \, T\) directed north is \(2.40 \times 10^{-12} \, N\).

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Most popular questions from this chapter

The conversion between atomic mass units and kilograms is $$1 \mathrm{u}=1.66 \times 10^{-27} \mathrm{kg}$$ Natural carbon consists of two different isotopes (excluding $^{14} \mathrm{C},$ which is present in only trace amounts). The isotopes have different masses, which is due to different numbers of neutrons in the nucleus; however, the number of protons is the same, and subsequently the chemical properties are the same. The most abundant isotope has an atomic mass of \(12.00 \mathrm{u} .\) When natural carbon is placed in a mass spectrometer, two lines are formed on the photographic plate. The lines show that the more abundant isotope moved in a circle of radius \(15.0 \mathrm{cm},\) while the rarer isotope moved in a circle of radius \(15.6 \mathrm{cm} .\) What is the atomic mass of the rarer isotope? (The ions have the same charge and are accelerated through the same potential difference before entering the magnetic field.)
The conversion between atomic mass units and kilograms is $$1 \mathrm{u}=1.66 \times 10^{-27} \mathrm{kg}$$ A sample containing sulfur (atomic mass 32 u), manganese \((55 \mathrm{u}),\) and an unknown element is placed in a mass spectrometer. The ions have the same charge and are accelerated through the same potential difference before entering the magnetic field. The sulfur and manganese lines are separated by \(3.20 \mathrm{cm},\) and the unknown element makes a line between them that is \(1.07 \mathrm{cm}\) from the sulfur line. (a) What is the mass of the unknown clement? (b) Identify the element.
A uniform magnetic field of \(0.50 \mathrm{T}\) is directed to the north. At some instant, a particle with charge \(+0.020 \mu \mathrm{C}\) is moving with velocity \(2.0 \mathrm{m} / \mathrm{s}\) in a direction \(30^{\circ}\) north of east. (a) What is the magnitude of the magnetic force on the charged particle? (b) What is the direction of the magnetic force?
In a certain region of space, there is a uniform electric field \(\overrightarrow{\mathbf{E}}=2.0 \times 10^{4} \mathrm{V} / \mathrm{m}\) to the east and a uniform magnetic field \(\overline{\mathbf{B}}=0.0050 \mathrm{T}\) to the west. (a) What is the electromagnetic force on an electron moving north at \(1.0 \times 10^{7} \mathrm{m} / \mathrm{s} ?(\mathrm{b})\) With the electric and magnetic fields as specified, is there some velocity such that the net electromagnetic force on the electron would be zero? If so, give the magnitude and direction of that velocity. If not, explain briefly why not.
(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.
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