Two fixed charges -4.0 C and -5.0 C, are separated a certain distance.
a) Is the net electric field at a location halfway between the two charges:
1) directed toward the -4.0 C charge
2) Zero
3) directed toward the -5.0 C charge
b) If the charges are separated by 20 cm, calculate the magnitude of the net electric field halfway between the two charges.
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a) The net electric field at a location halfway between two charges depends on the direction and magnitude of the individual electric fields produced by the charges.
Given that the charges have the same sign (-4.0 C and -5.0 C), the direction of the individual electric fields will be away from each other.
To determine the net electric field, we need to calculate the magnitudes of the individual electric fields due to each charge and then subtract them.
The magnitude of the electric field due to a point charge q at a distance r from the charge is given by the equation: E = k * |q| / r^2
Using Coulomb's law constant k = 9.0 x 10^9 Nm^2/C^2 and the given charges and distances, we can calculate the magnitude of the electric fields:
Electric field due to -4.0 C charge:
E1 = (9.0 x 10^9 Nm^2/C^2) * (4.0 C) / (distance^2)
Electric field due to -5.0 C charge:
E2 = (9.0 x 10^9 Nm^2/C^2) * (5.0 C) / (distance^2)
Since the charges are separated by the same distance, the magnitudes of the electric fields will be equal.
Therefore, the magnitude of the net electric field halfway between the two charges is zero.
Answer: 2) Zero
b) To calculate the magnitude of the net electric field halfway between the two charges, we use the equation:
E = E1 - E2
The distance halfway between the charges is half of the total distance, which is (20 cm / 2) = 10 cm = 0.1 m.
Using the magnitudes of the electric fields calculated in part a):
E = E1 - E2
E = (9.0 x 10^9 Nm^2/C^2) * (4.0 C) / (0.1 m)^2 - (9.0 x 10^9 Nm^2/C^2) * (5.0 C) / (0.1 m)^2
E = (9.0 x 10^9 Nm^2/C^2) * (4.0 C - 5.0 C) / (0.1 m)^2
E = (9.0 x 10^9 Nm^2/C^2) * (-1.0 C) / (0.1 m)^2
Simplifying:
E = (-9.0 x 10^9 Nm^2/C^2) * (1.0 C / (0.1 m)^2)
E = -9.0 x 10^11 N/C
Answer: The magnitude of the net electric field halfway between the two charges is 9.0 x 10^11 N/C.
To determine the net electric field at a location halfway between two charges, we need to take into account the electric fields created by each charge individually.
a) The direction of the net electric field at a location halfway between the two charges can be determined by comparing the magnitude of the electric fields created by each charge.
- If the electric field created by the -4.0 C charge is stronger than the electric field created by the -5.0 C charge, then the net electric field will be directed towards the -4.0 C charge.
- If the electric field created by the -5.0 C charge is stronger than the electric field created by the -4.0 C charge, then the net electric field will be directed towards the -5.0 C charge.
- If the magnitudes of the electric fields created by the two charges are equal, then the net electric field will be zero.
b) To calculate the magnitude of the net electric field halfway between the two 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 electrostatic constant (8.988 x 10^9 Nm^2/C^2), |q| is the magnitude of the charge, and r is the distance from the charge.
Let's calculate the magnitudes of the electric fields created by each charge first:
For the -4.0 C charge:
E1 = k * (|-4.0 C| / (0.20 m/2)^2)
E1 = k * (4.0 C / (0.10 m)^2)
For the -5.0 C charge:
E2 = k * (|-5.0 C| / (0.20 m/2)^2)
E2 = k * (5.0 C / (0.10 m)^2)
Once we have the magnitudes of the electric fields, we can compare them to determine the direction of the net electric field at the midpoint.
Finally, if the net electric field is not zero, we can calculate its magnitude by taking the difference between the magnitudes of the two electric fields:
|E_net| = |E1| - |E2|
Substituting the values of |E1| and |E2| calculated above will give us the magnitude of the net electric field.