Find the electric field at a point midway between two charges of +39.5 ✕ 10-9 C and +72.0 ✕ 10-9 C separated by a distance of 31.8 cm.
E = kq/r^2 where r is 1/2 .318m. Sum the effect of each vectorially. (note they're pushing in opposite directions.
l
To find the electric field at a point midway between two charges, we can use the principle of superposition. The electric field due to each individual charge can be separately calculated, and then added together to find the total electric field at the midpoint.
Let's label the charges as q1 = +39.5 ✕ 10^(-9) C and q2 = +72.0 ✕ 10^(-9) C. The distance between the charges is given as d = 31.8 cm = 0.318 m.
The formula for the electric field due to a point charge is given by:
E = (k * |q|) / r^2
where k is the Coulomb's constant (k = 8.99 ✕ 10^9 N.m^2/C^2), |q| is the absolute value of the charge, and r is the distance from the charge to the point where we want to find the electric field.
Step 1: Calculate the electric field due to the first charge (q1).
Using the formula, we have:
E1 = (k * |q1|) / (d/2)^2
where (d/2) is the distance from the first charge to the midpoint.
Plugging in the values, we get:
E1 = (8.99 ✕ 10^9 N.m^2/C^2 * |39.5 ✕ 10^(-9) C|) / (0.318 m / 2)^2
E1 = (8.99 ✕ 10^9 N.m^2/C^2 * 39.5 ✕ 10^(-9) C) / (0.159 m)^2
E1 = (8.99 ✕ 10^9 N.m^2/C^2 * 39.5 ✕ 10^(-9) C) / 0.0252 m^2
E1 = 0.564 N/C (rounded to three decimal places)
Step 2: Calculate the electric field due to the second charge (q2).
Using the same formula, we have:
E2 = (k * |q2|) / (d/2)^2
Plugging in the values, we get:
E2 = (8.99 ✕ 10^9 N.m^2/C^2 * |72.0 ✕ 10^(-9) C|) / (0.318 m / 2)^2
E2 = (8.99 ✕ 10^9 N.m^2/C^2 * 72.0 ✕ 10^(-9) C) / (0.159 m)^2
E2 = (8.99 ✕ 10^9 N.m^2/C^2 * 72.0 ✕ 10^(-9) C) / 0.0252 m^2
E2 = 2.372 N/C (rounded to three decimal places)
Step 3: Find the total electric field at the midpoint.
Since the electric fields due to the two charges are in the opposite direction, we subtract their magnitudes to find the net electric field at the midpoint.
E_total = |E1 - E2|
E_total = |0.564 N/C - 2.372 N/C|
E_total = 1.808 N/C (rounded to three decimal places)
Therefore, the electric field at a point midway between the two charges of +39.5 ✕ 10^(-9) C and +72.0 ✕ 10^(-9) C, separated by a distance of 31.8 cm, is approximately 1.808 N/C.
To find the electric field at a point midway between two charges, we can use the principle of superposition.
The electric field at a point due to each charge separately can be found using Coulomb's law, which states that the electric field created by a point charge is given by:
E = k * Q / r^2
Where E is the electric field, k is the electrostatic constant (k = 9 * 10^9 N*m^2/C^2), Q is the charge, and r is the distance from the charge to the point where we want to calculate the electric field.
In this case, we have two charges, +39.5 ✕ 10^-9 C and +72.0 ✕ 10^-9 C, separated by a distance of 31.8 cm. We want to find the electric field at a point midway between them.
Step 1: Convert the distance to meters:
31.8 cm = 31.8 * 10^-2 m = 0.318 m
Step 2: Calculate the electric field due to each charge separately:
E1 = k * Q1 / r^2
E2 = k * Q2 / r^2
Where Q1 = +39.5 ✕ 10^-9 C, Q2 = +72.0 ✕ 10^-9 C, and r = 0.318 m.
Step 3: Calculate the net electric field at the point midway between the charges.
Since the electric fields created by these charges are in the same direction, we can simply add them together:
E_total = E1 + E2
Step 4: Substitute the values and calculate the electric field.
E1 = (9 * 10^9 N*m^2/C^2) * (39.5 ✕ 10^-9 C) / (0.318 m)^2
E2 = (9 * 10^9 N*m^2/C^2) * (72.0 ✕ 10^-9 C) / (0.318 m)^2
E_total = E1 + E2
By substituting the values and performing the calculations, we can find the electric field at the point midway between the two charges.