Physics, 14.11.2019 04:31 jiiaxuan2035

Asingly charged ion of mass m is accelerated from rest by a potential difference δv. it is then deflected by a uniform magnetic field (perpendicular to the ion's velocity) into a semicircle of radius r. now a triply charged ion of mass m' is accelerated through the same potential difference and deflected by the same magnetic field into a semicircle of radius r' = 2r. what is the ratio of the masses of the ions?

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Answer from: eggemotions

m/m' = 1/12

Explanation:

First, we need to equal the kinetic energy with the electric potential energy to determine the first ion's velocity:

$\frac{1}{2} mv^{2} = q \Delta V$ (1)

where m: first ion's mass, v: first ion's velocity, q: first ion's charge and ΔV: potential difference

$v^{2} = \frac {2 q \Delta V}{m}$

$v = \sqrt {\frac {2 q \Delta V}{m}}$ (2)

To determine the mass m, we need to equal the centripetal force with the Lorentz force:

$ma_{c} = qvB = m \frac{v^{2}}{R}$

where $a_{c}$ : centripetal acceleration = v²/R, B: magnetic field, R: first ion's semicircle radius

$m = \frac {RqB}{v}$ (3)

From the equations (2) and (3), we can get the final expression for the mass m:

$m = \frac {RqB}{\sqrt {\frac {2 q \Delta V}{m}}}$

$m = \frac{R^{2} qB^{2}}{2 \Delta V}$ (4)

Similarly, for the second ion we have:

$m' = \frac{R'^{2} q'B^{2}}{2 \Delta V}$ (5)

Finally, from the equations (4) and (5), we can calculate the ratio of the masses of the ions:

$\frac {m}{m'} = \frac{R^{2} q}{R'^{2} q'} = \frac{R^{2} q}{(2R)^{2} \cdot 3q}$

$\frac {m}{m'} = \frac {1}{12}$

Have a nice day!

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

Answer from: Quest

Sorry i don’t know what to do

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Asingly charged ion of mass m is accelerated from rest by a potential difference δv. it is then defl...