What is the magnitude of the electric field at a point midway between a -5.1 microC and a +6.1 microC charge 10cm apart? Assume no other charges are nearby. What is the direction of the electric field?
To find the magnitude of the electric field at a point midway between two charges, you can use Coulomb's law and the principle of superposition. Coulomb's law states that the electric field between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The formula can be written as:
E = k(q1 * q2) / r^2
Where:
- E is the electric field
- k is the electrostatic constant (k ≈ 9 x 10^9 N m^2/C^2)
- q1 and q2 are the charges
- r is the distance between the charges.
In this case, the charges are -5.1 μC and +6.1 μC, and they are placed 10 cm (0.1 m) apart.
Step 1: Calculate the distance between the charges.
r = 0.1 m
Step 2: Calculate the electric field due to each charge.
E1 = k * (q1 * q3) / r^2
E2 = k * (q2 * q3) / r^2
Step 3: Use the principle of superposition to find the net electric field at the midpoint.
E = E1 + E2
Step 4: Determine the direction of the electric field.
The direction of the electric field is from the positive charge (+6.1 μC) to the negative charge (-5.1 μC), pointing towards the negative charge.
Now let's plug in the given values and calculate the magnitude of the electric field at the midpoint.
Step 1: Calculate the distance between the charges.
r = 0.1 m
Step 2: Calculate the electric field due to each charge.
E1 = (9 x 10^9 N m^2/C^2) * ((-5.1 x 10^-6 C) * (6.1 x 10^-6 C)) / (0.1 m)^2
E2 = (9 x 10^9 N m^2/C^2) * ((6.1 x 10^-6 C) * (-5.1 x 10^-6 C)) / (0.1 m)^2
Step 3: Use the principle of superposition to find the net electric field at the midpoint.
E = E1 + E2
Step 4: Determine the direction of the electric field.
The electric field is directed from the positive charge (+6.1 μC) to the negative charge (-5.1 μC), so it points towards the negative charge.
The calculated value of the electric field will give you the answer to both the magnitude and direction of the field at the midpoint between the charges.