<span>Last choice on the list:
Object A has a net charge of 0 because the positive and negative
charges are balanced.
Object B has a net charge of –2 because there is an imbalance of
charged particles (2 more negative electrons than positive protons).</span>
Explanation:
Let
is the mass of proton. It is moving in a circular path perpendicular to a magnetic field of magnitude B.
The magnetic force is balanced by the centripetal force acting on the proton as :
![\dfrac{mv^2}{r}=qvB](https://tex.z-dn.net/?f=%5Cdfrac%7Bmv%5E2%7D%7Br%7D%3DqvB)
r is the radius of path,
![r=\dfrac{mv}{qB}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7Bmv%7D%7BqB%7D)
Time period is given by :
![T=\dfrac{2\pi r}{v}](https://tex.z-dn.net/?f=T%3D%5Cdfrac%7B2%5Cpi%20r%7D%7Bv%7D)
![T=\dfrac{2\pi m_p}{qB}](https://tex.z-dn.net/?f=T%3D%5Cdfrac%7B2%5Cpi%20m_p%7D%7BqB%7D)
Frequency of proton is given by :
![f=\dfrac{1}{T}=\dfrac{qB}{2\pi m_p}](https://tex.z-dn.net/?f=f%3D%5Cdfrac%7B1%7D%7BT%7D%3D%5Cdfrac%7BqB%7D%7B2%5Cpi%20m_p%7D)
The wavelength of radiation is given by :
![\lambda=\dfrac{c}{f}](https://tex.z-dn.net/?f=%5Clambda%3D%5Cdfrac%7Bc%7D%7Bf%7D)
![\lambda=\dfrac{2\pi m_pc}{qB}](https://tex.z-dn.net/?f=%5Clambda%3D%5Cdfrac%7B2%5Cpi%20m_pc%7D%7BqB%7D)
So, the wavelength of radiation produced by a proton is
. Hence, this is the required solution.
Answer:
The inductor contains
loops
Explanation:
From the question we are told that
The capacitance of the capacitor is ![C = 286nF = 286 * 10^{-9} \ F](https://tex.z-dn.net/?f=C%20%3D%20%20286nF%20%3D%20286%20%2A%2010%5E%7B-9%7D%20%5C%20%20F)
The resonance frequency is ![f = 18.0 kHz = 18*10^{3} Hz](https://tex.z-dn.net/?f=f%20%3D%2018.0%20kHz%20%3D%20%2018%2A10%5E%7B3%7D%20Hz)
The diameter is ![d = 1.1 mm = \frac{1.1 }{1000} = 0.00011 \ m](https://tex.z-dn.net/?f=d%20%3D%20%201.1%20mm%20%3D%20%5Cfrac%7B1.1%20%7D%7B1000%7D%20%3D%200.00011%20%5C%20m)
The of the air-core inductor is ![l = 12 \ m](https://tex.z-dn.net/?f=l%20%3D%2012%20%5C%20m)
The permeability of free space is ![\mu_o = 4 \pi *10^{-7} \ T \cdot m/A](https://tex.z-dn.net/?f=%5Cmu_o%20%3D%204%20%5Cpi%20%2A10%5E%7B-7%7D%20%5C%20T%20%5Ccdot%20m%2FA)
Generally the inductance of this air-core inductor is mathematically represented as
![L = \frac{\mu_o * N^2 \pi d^2}{4 l}](https://tex.z-dn.net/?f=L%20%3D%20%20%5Cfrac%7B%5Cmu_o%20%2A%20N%5E2%20%5Cpi%20d%5E2%7D%7B4%20l%7D)
This inductance can also be mathematically represented as
![L = \frac{1}{w^2}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B1%7D%7Bw%5E2%7D)
Where
is the angular speed mathematically given as
![w = 2 \pi f](https://tex.z-dn.net/?f=w%20%3D%202%20%5Cpi%20f)
So
![L = \frac{1}{4 \pi ^2 f^2}](https://tex.z-dn.net/?f=L%20%3D%20%20%5Cfrac%7B1%7D%7B4%20%5Cpi%20%5E2%20f%5E2%7D)
Now equating the both formulas for inductance
![\frac{\mu_o * N^2 \pi d^2}{4 l} = \frac{1}{4 \pi ^2 f^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmu_o%20%2A%20N%5E2%20%5Cpi%20d%5E2%7D%7B4%20l%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B4%20%5Cpi%20%5E2%20f%5E2%7D)
making N the subject of the formula
![N = \sqrt{\frac{1}{(2 \pi f)^2} * \frac{4 * l }{\mu_o * \pi d^2 C} }](https://tex.z-dn.net/?f=N%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7B%282%20%5Cpi%20f%29%5E2%7D%20%2A%20%5Cfrac%7B4%20%2A%20l%20%7D%7B%5Cmu_o%20%2A%20%5Cpi%20d%5E2%20C%7D%20%20%7D)
![N = \frac{1}{2 \pi f} * \frac{2}{d} * \sqrt{\frac{l}{\pi * \mu_o * C} }](https://tex.z-dn.net/?f=N%20%3D%20%20%5Cfrac%7B1%7D%7B2%20%5Cpi%20f%7D%20%2A%20%5Cfrac%7B2%7D%7Bd%7D%20%2A%20%5Csqrt%7B%5Cfrac%7Bl%7D%7B%5Cpi%20%2A%20%5Cmu_o%20%2A%20C%7D%20%7D)
Substituting value
loops
Hydrogen, helium, and carbon.