A point charge of +4.6 micro-coulombs lies at x = 0 and a point charge of -7.3 micro-coulombs lies at x = +3.3 m. Where on the x axis, is the total electric potential equal to zero? Answer in meters.
a spherical gaussian surface of rdius R surrounds a point charge of magnitude +Q. How does the flux through the spherical surface change if the sign of the charge is reversed and the Gaussian sphere is doubled?
To find the location on the x-axis where the total electric potential is zero, we need to consider the contributions from both point charges.
The electric potential at a point due to a point charge is given by the equation:
V = k * q / r
where V is the electric potential, k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge to the point.
Let's first calculate the electric potential due to the +4.6 μC charge at x = 0:
V1 = k * q1 / r1
where q1 = +4.6 μC and r1 is the distance between the charge and the point. Since the point is on the x-axis, the distance is simply the absolute value of the x-coordinate.
Now, let's calculate the electric potential due to the -7.3 μC charge at x = 3.3 m:
V2 = k * q2 / r2
where q2 = -7.3 μC and r2 is the distance between the charge and the point. Again, the distance is the absolute value of the x-coordinate.
Since the total electric potential at a point is the sum of the electric potentials due to each charge, the condition for the total electric potential to be zero is:
V1 + V2 = 0
By substituting the respective values, we get:
(k * q1 / r1) + (k * q2 / r2) = 0
Simplifying the equation:
q1 / r1 = - (q2 / r2)
Now we can substitute the given values:
(4.6 x 10^-6 C) / x = - (7.3 x 10^-6 C) / (3.3 m - x)
To solve for x, we can cross-multiply the equation:
(4.6 x 10^-6 C)(3.3 m - x) = - (7.3 x 10^-6 C)(x)
Expanding and simplifying the equation:
15.18 x 10^-6 C - (4.6 x 10^-6 C)x = - (7.3 x 10^-6 C)x
15.18 x 10^-6 C = 7.3 x 10^-6 C + (4.6 x 10^-6 C)x
(4.6 x 10^-6 C)x = 15.18 x 10^-6 C - 7.3 x 10^-6 C
(4.6 x 10^-6 C)x = 7.88 x 10^-6 C
Dividing both sides by (4.6 x 10^-6 C):
x = (7.88 x 10^-6 C) / (4.6 x 10^-6 C)
x ≈ 1.71 m
Therefore, the total electric potential is equal to zero on the x-axis at approximately x = 1.71 meters.