What is the electric field midway between an electron and a proton separated by 0.7 nm?
To calculate the electric field midway between an electron and a proton, we can use Coulomb's law. Coulomb's law states that the electric force between two charged particles is directly proportional to the product of their charges, and inversely proportional to the square of the distance between them.
Let's break down the steps to solve the problem:
Step 1: Determine the charges of the electron and proton.
The charge of an electron (e) is equal to -1.6 x 10^-19 Coulombs.
The charge of a proton (p) is equal to +1.6 x 10^-19 Coulombs.
Step 2: Calculate the distance between the electron and proton.
The distance between the electron and proton is given as 0.7 nm. However, Coulomb's law requires the distance to be in meters. So, we need to convert 0.7 nm to meters.
1 nm = 1 x 10^-9 m
So, 0.7 nm = 0.7 x 10^-9 m = 7 x 10^-10 m
Step 3: Apply Coulomb's law.
Coulomb's law equation is given as:
F = (k * |q1 * q2|) / r^2
Where F is the electric force, k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between them.
In this case, we want to find the electric field midway between the electron and proton, which is the force experienced by a test charge at that location.
The electric field (E) is defined as the force (F) experienced by a test charge (q) per unit charge:
E = F / q
Since the test charge is typically 1 Coulomb, we can simplify the equation to:
E = F
Now we can substitute the values into Coulomb's law:
E = (k * |q1 * q2|) / r^2
Substituting the values:
E = (8.99 x 10^9 N m^2/C^2 * |(-1.6 x 10^-19 C) * (1.6 x 10^-19 C)|) / (7 x 10^-10 m)^2
Step 4: Calculate the electric field.
Performing the calculations:
E = (8.99 x 10^9 N m^2/C^2 * (1.6 x 10^-19 C) * (1.6 x 10^-19 C)) / (7 x 10^-10 m)^2
E = 7.4 x 10^18 N/C
Therefore, the electric field midway between an electron and a proton separated by 0.7 nm is approximately 7.4 x 10^18 N/C.
Twice the E-field due to the elctron alone.
Use Coulomb's law.
E = 2* k e/(R/2)^2 = 8 k e/R^2
where R is the separation of the two charges, and k is the Coulomb constant..