Two point charges are on the y-axis. A 3.0 µC charge is located at y = 1.35 cm, and a -2.04 µC charge is located at y = -1.50 cm.
(a) Find the total electric potential at the origin (V)
(b) Find the total electric potential at the point having coordinates (1.50 cm, 0). (V)
a) 0.000 m
To find the electric potential at a point, we need to use the equation for electric potential:
V = k * (q1/r1 + q2/r2 + q3/r3 + ...)
Where V is the electric potential, k is the Coulomb's constant (8.99 × 10^9 N m^2/C^2), q1, q2, q3, ... are the charges, and r1, r2, r3, ... are the distances between the charges and the point where we want to calculate the electric potential.
(a) To find the electric potential at the origin (0, 0), we need to calculate the electric potential contributed by both charges.
For the first charge, q1 = 3.0 µC, and the distance from the origin to this charge, r1, is 1.35 cm.
For the second charge, q2 = -2.04 µC, and the distance from the origin to this charge, r2, is -1.50 cm.
Plugging these values into the equation, we get:
V = k * (q1/r1 + q2/r2)
= ( 8.99 × 10^9 N m^2/C^2 ) * ( 3.0 × 10^(-6) C / 1.35 × 10^(-2) m + (-2.04 × 10^(-6) C / (-1.5 × 10^(-2) m) )
Calculating this expression will give the total electric potential at the origin (V).
(b) To find the electric potential at the point (1.50 cm, 0), we need to calculate the electric potential contributed by both charges.
For the first charge, q1 = 3.0 µC, and the distance from the point (1.50 cm, 0) to this charge, r1, can be found using the Pythagorean theorem. The coordinates of the point (1.50 cm, 0) form a right triangle with the y-axis and the line connecting the origin to the charge at y = 1.35 cm. The r1 can be calculated as:
r1 = sqrt( (1.35 cm)^2 + (1.50 cm)^2 )
For the second charge, q2 = -2.04 µC, and the distance from the point (1.50 cm, 0) to this charge, r2, can be found using the Pythagorean theorem. The coordinates of the point (1.50 cm, 0) form a right triangle with the y-axis and the line connecting the origin to the charge at y = -1.50 cm. The r2 can be calculated as:
r2 = sqrt( (-1.5 cm)^2 + (1.5 cm)^2 )
Plugging these values into the equation, we get:
V = k * (q1/r1 + q2/r2)
= ( 8.99 × 10^9 N m^2/C^2 ) * ( 3.0 × 10^(-6) C / r1 + (-2.04 × 10^(-6) C / r2) )
Calculating this expression will give the total electric potential at the point (1.50 cm, 0) (V).