To find the charge, we need to use the formula for the electric field strength of a dipole:
E = k * |p| / r^3,
where E is the electric field strength, k is the electrostatic constant (k ≈ 9 × 10^9 N m^2 / C^2), |p| is the magnitude of the electric dipole moment, and r is the distance between the point and the center of the dipole.
First, let's find the magnitude of the electric dipole moment |p|:
|p| = q * d,
where q is the charge and d is the distance between the charges.
We know that the distance between the charges is 1.00 cm, so |p| = q * 0.01 m.
Now let's find the distance between the point (0 cm, 10 cm) and the center of the dipole:
r = sqrt(x^2 + y^2) = sqrt(0^2 + 0.1^2) = 0.1 m.
Now we can plug in the known values into the formula for the electric field strength:
320 N/C = (9 × 10^9 N m^2 / C^2) * (q * 0.01 m) / (0.1 m)^3.
Solving for q, we get:
q ≈ 1.07 nC.
Now let's find the electric field strength at the point (x, y) = (10 cm, 0 cm).
First, let's find the distance between the point and the center of the dipole:
r = sqrt(x^2 + y^2) = sqrt(0.1^2 + 0^2) = 0.1 m.
Now we can plug in the known values and the charge q into the formula for the electric field strength:
E = (9 × 10^9 N m^2 / C^2) * (1.07 nC * 0.01 m) / (0.1 m)^3.
Calculating the electric field strength, we get:
E ≈ 32 N/C.
An electric dipole is formed from two charges, ±q, spaced 1.00cm apart. The dipole is at the origin, oriented along the y-axis. The electric field strength at the point (x,y)=(0cm,10cm) is 320N/C .
What is the charge q? Give your answer in nC.
What is the electric field strength at the point (x,y)=(10cm,0cm)?
1 answer