How Close Can a Proton Get to a Charged Sphere?

[AnthroMecha]

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

 

[SammyS]

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?

 

[AnthroMecha]

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

 

[SammyS]

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 ?

 

[AnthroMecha]

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. :(