How Close Can a Proton Get to a Charged Sphere?

AI Thread Summary
A proton with an initial velocity of 6.28x10^5 m/s approaches a charged conducting sphere with a radius of 85.2 cm and a charge of 4.83 μC. The key equations for solving the problem include kinetic energy and electric potential, specifically 1/2mv^2 = -qΔV. The electric potential at the sphere's surface is calculated to be approximately 50964.4V, though there is uncertainty about the correct application of the equations. The discussion highlights the need to determine the distance from the proton to the sphere's center to find the potential at the proton's initial location. The participant expresses concern about the complexity of the problem and its relevance to an upcoming test.
AnthroMecha
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Homework Statement



A proton is moving with an initial velocity of 6.28x10^5 m/s straight towards a large conducting
sphere of radius 85.2 cm. The sphere has a charge of 4.83 μC on it. Protons have a mass of
1.69x10^-27 kg.

a) Determine how close the proton can come to the surface of the sphere.
b) What is the voltage on the surface of the sphere?


Homework Equations



possibly 1/2mv^2=-qΔV

The Attempt at a Solution



Don't even know where to begin on this one
 
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AnthroMecha said:

Homework Statement



A proton is moving with an initial velocity of 6.28x10^5 m/s straight towards a large conducting
sphere of radius 85.2 cm. The sphere has a charge of 4.83 μC on it. Protons have a mass of
1.69x10^-27 kg.

a) Determine how close the proton can come to the surface of the sphere.
b) What is the voltage on the surface of the sphere?

Homework Equations



possibly 1/2mv^2=-qΔV

The Attempt at a Solution



Don't even know where to begin on this one
That's a good relevant equation, since at closest approach, the proton's velocity will be zero.

What is the electric potential at the location of the proton, due to the sphere?
 
SammyS said:
That's a good relevant equation, since at closest approach, the proton's velocity will be zero.

What is the electric potential at the location of the proton, due to the sphere?

I'm coming up with 50964.4V electric potential (I may be using the wrong equation).

I used V=(1/(4πε0))(q/r)

q=4.83μC, r=85.2cm
 
AnthroMecha said:
I'm coming up with 50964.4V electric potential (I may be using the wrong equation).

I used V=(1/(4πε0))(q/r)

q=4.83μC, r=85.2cm
That's good for part (b).

To find the potential due to the sphere at the location of the proton at the time its velocity is 6.28×105 m/s, you have to know how far the proton is from the center of the sphere at that time.

Did they give that quantity ?
 
SammyS said:
That's good for part (b).

To find the potential due to the sphere at the location of the proton at the time its velocity is 6.28×105 m/s, you have to know how far the proton is from the center of the sphere at that time.

Did they give that quantity ?

no. I'm wondering if it involves some sort of integral. I hope there's nothing like this one on the test, because I have to go take it in an hour, lol! I kind of procrastinated a bit on this one. :(
 

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