Explanation:
Gauss Law relates the distribution of electric charge to the resulting electric field.
Applying Gauss's Law,
EA = Q / ε₀
Where:
E is the magnitude of the electric field,
A is the cross-sectional area of the conducting sphere,
Q is the positive charge
ε₀ is the permittivity
We be considering cases for the specified regions.
<u>Case 1</u>: When r < R
The electric field is zero, since the enclosed charge is equal to zero
E(r) = 0
<u>Case 2</u>: When R < r < 2R
The enclosed charge equals to Q, then the electric field equals;
E(4πr²) = Q / ε₀
E = Q / 4πε₀r²
E = KQ /r²
Constant K = 1 / 4πε₀ = 9.0 × 10⁹ Nm²/C²
<u>Case 3</u>: When r > 2R
The enclosed charge equals to Q, then the electric field equals;
E(4πr²) = 2Q / ε₀
E = 2Q / 4πε₀r²
E = 2KQ /r²
To solve this problem it is necessary to use the concepts related to the Gravitational Force and Newton's Second Law, as far as we know:
Where,
G = Gravitational constant
M = Mass of earth (in this case)
m = mass of satellite
r = radius
In the other hand we have the second's newton law:
Where,
m = mass
a = acceleration
Equation both equations we have,
For the problem we have that,
<em>Satellite A:</em>
<em>Satellite B:</em>
The ratio between the two satellites would be,
Solving for a_B,
Therefore the centripetal acceleration of 
is a quarter of 
Potential energy is the energy possessed by a body at rest while the kinetic energy is the energy possessed by a body in motion.
Potential energy is given by mass× gravitational acceleration × height
That is energy = mgh
For the first ball the potential energy is 2.268 ×10 ×5 = 113.4 J (5 lb = 2.268 kg)
The second ball with the same mass will have 2.268 ×10 ×10 = 226.8 J
Thus, the potential energy is dependent on the height of a given body and therefore the ball at the 5 foot hill has less potential energy.
