Two positive charges of 6.83 µC each are
673 cm apart.
Find the electric field midway between
them. The value of the Coulomb constant
is 8.98755 × 10
9
N · m2
/C
2
.
To find the electric field midway between two positive charges, you can use the formula:
Electric field (E) = (k * Q) / r^2
Where:
- k is the Coulomb constant (8.98755 × 10^9 N·m^2/C^2)
- Q is the charge of each positive charge (6.83 µC or 6.83 × 10^-6 C)
- r is the distance between the two charges (673 cm or 6.73 m)
First, calculate the electric field due to one of the charges at the midpoint:
E1 = (k * Q) / (r/2)^2
Substituting the values into the equation:
E1 = (8.98755 × 10^9 N·m^2/C^2 * 6.83 × 10^-6 C) / (6.73 m/2)^2
Simplifying the expression inside the parentheses:
E1 = (8.98755 × 10^9 N·m^2/C^2 * 6.83 × 10^-6 C) / (3.365 m)^2
Calculate the value inside the parentheses:
E1 = (8.98755 × 10^9 N·m^2/C^2 * 6.83 × 10^-6 C) / 11.312225 m^2
Simplify the expression:
E1 = (8.98755 × 6.83 × 10^9) / 11.312225 N/C
Next, since the electric fields due to the two charges are in the same direction, you can double the previous result to find the net electric field at the midpoint:
E_net = 2 * E1
Substituting the value of E1:
E_net = 2 * (8.98755 × 6.83 × 10^9) / 11.312225 N/C
Calculating the expression:
E_net = (17.9751 × 6.83 × 10^9) / 11.312225 N/C
E_net = 122.824025 × 10^9 / 11.312225 N/C
Simplifying:
E_net = 10.8425873 × 10^9 N/C
Therefore, the electric field midway between the two positive charges is approximately 10.8425873 × 10^9 N/C.
To find the electric field midway between the two positive charges, we can use the formula for electric field due to a point charge:
E = k * (q / r^2)
Where:
- E is the electric field
- k is the Coulomb constant (8.98755 × 10^9 N · m^2 / C^2)
- q is the charge
- r is the distance from the charge
In this case, we have two positive charges of 6.83 µC each, and they are 673 cm apart. Since we want to find the electric field midway between them, the distance from each charge to the midpoint would be half of 673 cm, which is 336.5 cm.
Now, let's convert the charge from microcoulombs to coulombs:
1 µC = 1 × 10^(-6) C
Therefore, each charge is 6.83 × 10^(-6) C.
We can now substitute the values into the equation to find the electric field:
E = k * (q / r^2)
E = 8.98755 × 10^9 N · m^2 / C^2 * (6.83 × 10^(-6) C) / (0.3365 m)^2
Calculating this expression will give us the value of the electric field at the midpoint between the two charges.