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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, 胃 = 90掳 (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掳 (perpendicular), the sine function is as follows: \(\sin\theta = \sin 90掳 = 1\)
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

A charged particle is accelerated from rest through a potential difference \(\Delta V\). The particle then passes straight through a velocity selector (field magnitudes \(E\) and \(B\) ). Derive an expression for the charge-to-mass ratio \((q / m)\) of the particle in terms of \(\Delta V, E,\) and \(B\)

An electromagnetic rail gun can fire a projectile using a magnetic field and an electric current. Consider two conducting rails that are \(0.500 \mathrm{m}\) apart with a \(50.0-\mathrm{g}\) conducting rod connecting the two rails as in the figure with Problem \(46 .\) A magnetic field of magnitude \(0.750 \mathrm{T}\) is directed perpendicular to the plane of the rails and rod. A current of \(2.00 \mathrm{A}\) passes through the rod. (a) What direction is the force on the rod? (b) If there is no friction between the rails and the rod, how fast is the rod moving after it has traveled \(8.00 \mathrm{m}\) down the rails?
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?
An electromagnetic flowmeter is to be used to measure blood speed. A magnetic field of \(0.115 \mathrm{T}\) is applied across an artery of inner diameter \(3.80 \mathrm{mm}\) The Hall voltage is measured to be \(88.0 \mu \mathrm{V} .\) What is the average speed of the blood flowing in the artery?
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.
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