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3 years ago

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A proton travels at a speed of 2.0 × 106 meters/second. Its velocity is at right angles with a magnetic field of strength 5.5 ×

10-3 tesla. What is the magnitude of the magnetic force on the proton?

1 answer:

Finger [1]3 years ago

6 0

So here we are given that the the velocity of the proton ( V ) is 2.0 × $10^6$ meters / second, with a magnetic field of strength 5.5 × $10^{-3}$ tesla. If they each form a right angle, they are hence perpendicular to one another, such that ....

F = q( V × B ),

F = q v B( sin ∅ ),

F = q v B( sin( 90 ) )

.... they form the following formula. Let's go through each of the variables in our formula here -

{ F = Magnetic Force ( which has to be calculated ), q = charge of proton (has charge of 1.602 × $10^{19}$ coulombs ), B = magnetic field }

All we have to do now is plug and chug,

F = ( 1.602 × $10^{19}$ )( 2.0 × $10^6$ )( 5.5 × $10^{-3}$ ) = ( About ) 1.8 × $10^{-15}$ Newtons

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Answer:

a) $T_{2} = 360.955\,K$ , $P_{2} = 138569.171\,Pa\,(1.386\,bar)$ , b) $T_{2} = 347.348\,K$ , $V_{2} = 0.14\,m^{3}$

Explanation:

a) The ideal gas is experimenting an isocoric process and the following relationship is used:

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$Q = n\cdot \bar c_{v}\cdot (T_{2}-T_{1})$

$T_{2} = T_{1} + \frac{Q}{n\cdot \bar c_{v}}$

The number of moles of the ideal gas is:

$n = \frac{P_{1}\cdot V_{1}}{R_{u}\cdot T_{1}}$

$n = \frac{\left(101,325\,Pa + \frac{(200\,kg)\cdot (9.807\,\frac{m}{s^{2}} )}{0.15\,m^{2}} \right)\cdot (0.12\,m^{3})}{(8.314\,\frac{Pa\cdot m^{3}}{mol\cdot K} )\cdot (298\,K)}$

$n = 5.541\,mol$

The final temperature is:

$T_{2} = 298\,K +\frac{10,500\,J}{(5.541\,mol)\cdot (30.1\,\frac{J}{mol\cdot K} )}$

$T_{2} = 360.955\,K$

The final pressure is:

$P_{2} = \frac{T_{2}}{T_{1}}\cdot P_{1}$

$P_{2} = \frac{360.955\,K}{298\,K}\cdot \left(101,325\,Pa + \frac{(200\,kg)\cdot (9.807\,\frac{m}{s^{2}} )}{0.15\,m^{2}}\right)$

$P_{2} = 138569.171\,Pa\,(1.386\,bar)$

b) The ideal gas is experimenting an isobaric process and the following relationship is used:

$\frac{T_{1}}{V_{1}} = \frac{T_{2}}{V_{2}}$

Final temperature is cleared from this expression:

$Q = n\cdot \bar c_{p}\cdot (T_{2}-T_{1})$

$T_{2} = T_{1} + \frac{Q}{n\cdot \bar c_{p}}$

$T_{2} = 298\,K +\frac{10,500\,J}{(5.541\,mol)\cdot (38.4\,\frac{J}{mol\cdot K} )}$

$T_{2} = 347.348\,K$

The final volume is:

$V_{2} = \frac{T_{2}}{T_{1}}\cdot V_{1}$

$V_{2} = \frac{347.348\,K}{298\,K}\cdot (0.12\,m^{3})$

$V_{2} = 0.14\,m^{3}$

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