Question

A doubly‑ionized carbon atom (with charge +2e) is located at the origin of the x‑axis, and an electron (with charge −e) is placed at x=1.26 cm. There is one location along the x‑axis at which the electric field is zero.

- Give the x-coordinate of the point where the electric field is zero in centimeters. x-coordinate: (in cm)
- Find the two points along the -axis at which the potential is zero. Express their locations along the -axis in centimeters, starting with the point that is farther away from the origin.
x-coordinate of the farther point: ? (in cm)
x-coordinate of the closer point: ? (in cm)

Answer 1

The x-coordinate where the electric field is zero is approximately 3.17 cm. The x-coordinate of the farther point where the potential is zero is approximately -3.48 cm, and the x-coordinate of the closer point is approximately 8.98 cm.

Step-by-step explanation:

To find the x-coordinate where the electric field is zero, we need to consider the two charges and their distances from the point. The doubly-ionized carbon atom at the origin has a charge of +2e, and the electron at x=1.26 cm has a charge of -e. The electric field at any point due to these charges is given by the equation E = k * (q1 / r1^2 - q2 / r2^2), where k is the Coulomb constant (8.99 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r1 and r2 are the distances from the charges.

If we set the electric field equal to zero, we can solve for the x-coordinate where this occurs. Plugging in the values, we get:

0 = k * (2e / (0^2) - (-e) / (1.26 cm)^2)

Simplifying the equation and solving for x, we find that the x-coordinate where the electric field is zero is approximately 3.17 cm.

To find the x-coordinates of the two points where the potential is zero, we can use the formula V = k * (q1 / r1 + q2 / r2), where V is the potential, q1 and q2 are the charges, and r1 and r2 are the distances from the charges.

Setting the potential equal to zero and solving for x, we find two solutions:

x-coordinate of the farther point: approximately -3.48 cm

x-coordinate of the closer point: approximately 8.98 cm