An electric dipole lies on the x-axis, consisting of a -2.3nC charge at x = -11cm and a +2.3nC charge at x = 11cm .
Part A
Compute the electric field at the point (–16cm , 0). Find the magnitude of the electric field.
Express your answer to two significant figures and include the appropriate units.
Part B
Compute the electric field at the point (0, –7cm ). Find the magnitude of the electric field.
Express your answer to two significant figures and include the appropriate units.
To calculate the electric field at a given point due to an electric dipole, we need to consider the contribution from each charge in the dipole and then add them up vectorially.
The formula for the electric field due to a point charge at a distance "r" is given by:
E = k * (q / r^2)
where E is the electric field, k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2), q is the charge, and r is the distance between the point charge and the point where we want to calculate the electric field.
Let's proceed with the calculations for Part A:
Given the dipole configuration:
- Charge q1 = -2.3 nC located at x1 = -11 cm
- Charge q2 = +2.3 nC located at x2 = 11 cm
- We want to find the electric field at point P with coordinates (x, y) = (-16 cm, 0 cm).
Step 1: Calculate the electric field contribution due to the first charge (q1):
Using the formula:
E1 = k * (q1 / r1^2)
Using the given values:
q1 = -2.3 nC
r1 = |-16 cm - (-11 cm)| = 5 cm
Substituting these values into the formula for E1:
E1 = (9 x 10^9 Nm^2/C^2) * (-2.3 x 10^-9 C) / (0.05 m)^2
E1 = -0.092 N/C
The electric field due to the first charge is -0.092 N/C directed towards the positive x-axis.
Step 2: Calculate the electric field contribution due to the second charge (q2):
Using the formula:
E2 = k * (q2 / r2^2)
Using the given values:
q2 = +2.3 nC
r2 = |(-16 cm) - (+11 cm)| = 27 cm
Converting the distance to meters:
r2 = 0.27 m
Substituting these values into the formula for E2:
E2 = (9 x 10^9 Nm^2/C^2) * (2.3 x 10^-9 C) / (0.27 m)^2
E2 = 0.095 N/C
The electric field due to the second charge is 0.095 N/C directed towards the negative x-axis.
Step 3: Calculate the total electric field at the point P:
To find the total electric field at P, we need to add up the electric field contributions from both charges:
E_total = E1 + E2
E_total = -0.092 N/C + 0.095 N/C
E_total = 0.003 N/C
The total electric field at point P is 0.003 N/C directed towards the negative x-axis.
Now, let's move on to Part B:
Given the dipole configuration remains the same:
- Charge q1 = -2.3 nC located at x1 = -11 cm
- Charge q2 = +2.3 nC located at x2 = 11 cm
- We want to find the electric field at point P with coordinates (x, y) = (0 cm, -7 cm).
Step 1: Calculate the distance between the two charges:
r = |x2 - x1|
r = |11 cm - (-11 cm)|
r = 22 cm
r = 0.22 m
Step 2: Calculate the electric field contribution due to the first charge (q1):
Using the formula:
E1 = k * (q1 / r1^2)
Using the given values:
q1 = -2.3 nC
r1 = |y - x1|
r1 = |-7 cm - (-11 cm)|
r1 = 4 cm
r1 = 0.04 m
Substituting these values into the formula for E1:
E1 = (9 x 10^9 Nm^2/C^2) * (-2.3 x 10^-9 C) / (0.04 m)^2
E1 = -13.58 N/C
The electric field due to the first charge is -13.58 N/C directed towards the negative y-axis.
Step 3: Calculate the electric field contribution due to the second charge (q2):
Using the formula:
E2 = k * (q2 / r2^2)
Using the given values:
q2 = +2.3 nC
r2 = |y - x2|
r2 = |-7 cm - 11 cm|
r2 = -18 cm
r2 = 0.18 m
Substituting these values into the formula for E2:
E2 = (9 x 10^9 Nm^2/C^2) * (2.3 x 10^-9 C) / (0.18 m)^2
E2 = 13.58 N/C
The electric field due to the second charge is 13.58 N/C directed towards the positive y-axis.
Step 4: Calculate the total electric field at point P:
To find the total electric field at P, we need to add up the electric field contributions from both charges:
E_total = E1 + E2
E_total = -13.58 N/C + 13.58 N/C
E_total = 0 N/C
The total electric field at point P is 0 N/C.