Solving for r: Finding Electric Field When Gravitational Fields Equal Zero

AI Thread Summary
To find the electric field (E) when gravitational forces equal zero, one must consider the balance of forces acting on a proton in a uniform electric field. The gravitational force, calculated using w=mg, must equal the electrostatic force, which can be derived from the electric field. The discussion highlights that the radius (r) is not necessary for calculating the electric field's magnitude, as the focus is on the equilibrium of forces. Participants emphasize understanding the relationship between electric and gravitational forces rather than relying on specific formulas. Ultimately, the key takeaway is that the electric field can be determined without knowing the radius.
hippolyta2078795
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A proton(m=1.67 * 10^-27 kg) is suspended at rest in a uniform electric field E. Take into account gravity and determine E.

How do I find the field if I don't know what r is.

A spacecraft makes a trip from the Earth to the Moon, 380000km away. At what point in the trip will the gravitational field be zero? The mass of the Moon is about 1/81 that of Earth.

I understand this problem I think, but I want to make sure. I plug the numbers in for Newton's universal gravitation law. I have to fields, one exerted by the Earth, one by the moon. I set the radius in the moon's field as (380000000-r)meters. Right?
 
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What you are doing in the first problem is looking at two balanced forces. One of the forces is weight (force due to gravity) which is found by w=mg. The other force is the electrstatic force which can similary be found by multiplying two things together.Second one, yes you are on the right track. You will get to a point where it might look like the quadratic formula will come up, but...
"cross multiply and square root both sides." Saves a lot of time.
 
What are those things. I don't know how to find the magnitude of a field with an unknown radius. Thanks.
 
hippolyta2078795 said:
What are those things. I don't know how to find the magnitude of a field with an unknown radius. Thanks.
You don't need the radius for calculate this electric field.

It more clear with the anterior aclaration, specialy the one that say something like "its about 2 forces in equilibrium".
The electric field is not a force at all, but a description of how the force (electric one) interact with the environment more clearly with other electric charges (correct me some one if I am wrong). In short you will not use the formula for the electric field, but calculate the "magnitude".

Or a hint, you can use a deduction the one that goes from show how to get the electric field from the electric force, the answer of what you need is there also the formula (that you don't need here is there).
 
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