Consider a point charge with q = 1.510-8 C. (a) What is the radius of an equipotential surface having a potential of 30 V? (b) Are surfaces whose potential differ by a constant amount (1.0 V) evenly spaced in radius
To answer both parts of the question, we need to use the equation for the electric potential of a point charge, which is given by:
V = k * q / r
where:
V is the electric potential,
k is Coulomb's constant (k = 8.99 * 10^9 N m^2/C^2),
q is the charge, and
r is the distance from the point charge.
Now let's solve each part of the question:
(a) To find the radius of an equipotential surface with a potential of 30 V, we can rearrange the formula and solve for r:
V = k * q / r
30 = (8.99 * 10^9) * (1.5 * 10^-8) / r
To isolate r, we can multiply both sides of the equation by r and divide both sides by 30:
30 * r = (8.99 * 10^9) * (1.5 * 10^-8)
r = (8.99 * 10^9) * (1.5 * 10^-8) / 30
Calculating this expression will give us the radius of the equipotential surface.
(b) Are surfaces with a constant potential difference of 1.0 V evenly spaced in radius?
To answer this, we need to examine the equation for electric potential and see if surfaces with different potentials are evenly spaced in radius. From the equation:
V = k * q / r
We can see that the potential is inversely proportional to the distance from the charge (r). As r decreases, V increases, and vice versa. Therefore, surfaces with different potentials will not be evenly spaced in radius.
In other words, the potential difference between two surfaces that are 1.0 V apart will depend on their initial radius and it will change as we move to a different radius.
Therefore, surfaces with a constant potential difference of 1.0 V will not be evenly spaced in radius.