Question

An electron and a proton are fixed at a separation distance of 963 nm. Find the magnitude and direction of the electric field at their midpoint

Answer 1

The magnitude of the electric field at the midpoint between a proton and an electron is 0 N/C, and there is no direction, because the electric fields due to both particles cancel each other out.

Step-by-step explanation:

To find the magnitude and direction of the electric field at the midpoint between a proton and an electron, we can apply the principle of superposition for electric fields. Since a proton and electron have equal but opposite charges, the electric field from each at the midpoint will have the same magnitude but opposite direction. Because they are equal in magnitude, the electric fields will cancel each other out at the midpoint, resulting in a net electric field of zero.

Here's the step-by-step approach:

1. Calculate the electric field due to the electron (Ee) at the midpoint using Coulomb's Law: Ee = k * |q| / (r^2), where 'k' is Coulomb's constant (8.99 x 10^9 Nm^2/C^2), '|q|' is the magnitude of the charge on the electron (1.6 x 10^-19 C), and 'r' is the distance from the electron to the midpoint (481.5 nm or 481.5 x 10^-9 m).
2. Calculate the electric field due to the proton (Ep) at the midpoint using the same formula, noting that the charge magnitude is the same but the direction is opposite to that of the electron.
3. Because the electron and proton have opposite charges, the electric fields at the midpoint will point in opposite directions. For a positive charge, the field points away, and for a negative charge, it points towards. Thus, the electric fields due to the electron and proton at the midpoint are in opposite directions and cancel each other out.

Therefore, the magnitude of the electric field at the midpoint is 0 N/C, and there is no direction to indicate since the field is nonexistent.