Electrostatics Question

[discowisco]

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An electron gun uusually consists of two electrode plates, one more negatively charged than the other. If an eletron of mass m is allowed to accelerate between the two electrodes separated by a voltage V, which equation BEST represents the final speed of the intially stationary electron upon striking the more positive electrode?

v = sqrt (m/ 2ev)
v = sqrt (2ev/ m)
v = sqrt (mv/ 2e)
v = sqrt (2e/ m)

How do you approach this? Initially doesnt the electron have potential energy? TBR says it has no energy initially since its at rest.

 

[discowisco]

The way I figured was I know that Initial + Work = Final so final is 1/2mv^2 and that Work is -dPE = -qv

...so shouldnt it be -qv= 1/2mv^2 then solve for v. In the book they have ev=1/2mv^2 then solved for v

I understand that they substituted e in for q since its an electron but then wouldnt it be -ev= 1/2mv^2

And how is intial energy 0, I thought it would have potential energy

 

[circulus vitios]

The way I figured was I know that Initial + Work = Final so final is 1/2mv^2 and that Work is -dPE = -qv

...so shouldnt it be -qv= 1/2mv^2 then solve for v. In the book they have ev=1/2mv^2 then solved for v

I understand that they substituted e in for q since its an electron but then wouldnt it be -ev= 1/2mv^2

And how is intial energy 0, I thought it would have potential energy

"q" is always assumed to be positively charged. Electrons are negatively charged, thus the sign reversal?

 

[LianaStan]

The initial energy is zero b/c the equation you gave is the work energy theorem which concerns work & kinetic energy. The electric field does work on the electron which increases its initial KE from 0 to KE=W=eV.

The easy answer for why the e is not negative is that it is convention to take the absolute value of the charge when calculating the energy U=qV. I believe the more complicated answer involves switching of the voltage sign to cancel out the negative charge for the electron, though I am not sure on this answer as the details of the concept escape me.

 

[gtbROX]

An electron gun uusually consists of two electrode plates, one more negatively charged than the other. If an eletron of mass m is allowed to accelerate between the two electrodes separated by a voltage V, which equation BEST represents the final speed of the intially stationary electron upon striking the more positive electrode?

v = sqrt (m/ 2ev)
v = sqrt (2ev/ m)
v = sqrt (mv/ 2e)
v = sqrt (2e/ m)

How do you approach this? Initially doesnt the electron have potential energy? TBR says it has no energy initially since its at rest.

Kinetic Energy (KE) is the energy in movement, and potential energy (PE) is generally stored energy. TBR probably meant that it had no Kinetic energy meaning it started at v=0. Energy can definitely be converted so you just have to set the PE (qV) equal to KE (1/2mv^2).