Suppose you have a 3 C charge at (1,0) m and a -3 C charge at (-1,0) m. Find (a) the electric field at the point (0,3), and (b) the electric force on a charge of 3 nC placed at (0,3).
To find the electric field at a point due to two point charges, we can use the formula:
E = k * q / r^2
Where:
- E is the electric field vector,
- k is the Coulomb's constant (9 * 10^9 Nm^2/C^2),
- q is the magnitude of the charge,
- r is the distance between the point charge and the point where we want to find the electric field.
Let's calculate the electric field at point (0,3) using the given charges:
For the 3 C charge at (1,0) m:
- Magnitude of the charge (q1) = 3 C
- Distance from the point (0,3) to (1,0) is r1 = sqrt((0-1)^2 + (3-0)^2) = sqrt(10) m
For the -3 C charge at (-1,0) m:
- Magnitude of the charge (q2) = -3 C
- Distance from the point (0,3) to (-1,0) is r2 = sqrt((0+1)^2 + (3-0)^2) = sqrt(10) m
Now, let's calculate the electric field at point (0,3) due to each charge.
For the 3 C charge at (1,0) m:
E1 = k * q1 / r1^2 = (9 * 10^9 Nm^2/C^2) * (3 C) / (sqrt(10) m)^2
For the -3 C charge at (-1,0) m:
E2 = k * q2 / r2^2 = (9 * 10^9 Nm^2/C^2) * (-3 C) / (sqrt(10) m)^2
The total electric field at point (0,3) is the vector sum of the two electric fields:
E_total = E1 + E2
To find the electric force on a charge at the point (0,3), we can use the formula:
F = q * E
Where:
- F is the electric force vector,
- q is the magnitude of the charge,
- E is the electric field vector.
Let's calculate the electric force on a charge of 3 nC placed at (0,3) using the electric field E_total we calculated earlier.
F = (3 * 10^-9 C) * E_total
Now you can substitute the values and calculate both the electric field and the electric force.