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jolli1 [7]
3 years ago
8

An electron of kinetic energy 1.59 keV circles in a plane perpendicular to a uniform magnetic field. The orbit radius is 35.4 cm

. Find (a) the electron's speed, (b) the magnetic field magnitude, (c) the circling frequency, and (d) the period of the motion.
Physics
1 answer:
Blizzard [7]3 years ago
8 0

Answer:

a) v = 2.36 \cdot 10^{7} m/s

b) B = 3.80 \cdot 10^{-4} T

c) f = 1.06 \cdot 10^{7} Hz

d) T = 9.43 \cdot 10^{-8} s

Explanation:

a) We can find the electron's speed by knowing the kinetic energy:

K = \frac{1}{2}mv^{2}

Where:    

K: is the kinetic energy = 1.59 keV

m: is the electron's mass = 9.11x10⁻³¹ kg

v: is the speed =?

v = \sqrt{\frac{2K}{m}} = \sqrt{\frac{2*1.59 \cdot 10^{3} eV*\frac{1.602 \cdot 10^{-19} J}{1 eV}}{9.11 \cdot 10^{-31} kg}} = 2.36 \cdot 10^{7} m/s

b) The electron's speed can be found by using Lorentz's equation:

F = q(v\times B) = qvBsin(\theta)   (1)

Where:

F: is the magnetic force

q: is the electron's charge = 1.6x10⁻¹⁹ C

θ: is the angle between the speed of the electron and the magnetic field = 90°

The magnetic force is also equal to:

F = ma_{c} = m\frac{v^{2}}{r}   (2)

By equating equation (2) with (1) and by solving for B, we have:

B = \frac{mv}{rq} = \frac{9.11 \cdot 10^{-31} kg*2.36 \cdot 10^{7} m/s}{0.354 m*1.6 \cdot 10^{-19} C} = 3.80 \cdot 10^{-4} T

c) The circling frequency is:

f = \frac{1}{T} = \frac{\omega}{2\pi} = \frac{v}{2\pi r}

Where:

T: is the period = 2π/ω

ω: is the angular speed = v/r

f = \frac{v}{2\pi r} = \frac{2.36 \cdot 10^{7} m/s}{2\pi*0.354 m} = 1.06 \cdot 10^{7} Hz

d) The period of the motion is:

T = \frac{1}{f} = \frac{1}{1.06 \cdot 10^{7} Hz} = 9.43 \cdot 10^{-8} s

I hope it helps you!

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Answer:

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Explanation:

The reaction equation is given as:

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The problem at hand is to balance this chemical reaction. To solve this problem we use a mathematical approach;

        aKI   +  bCl₂   →    cKCl     +    dI₂

 Conserving K : a = c

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Answer:

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Explanation:

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similarly final position vector is given as

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now the displacement of the object is given as

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