two point charges are 10.0 cm apart and have chargeso of 2.0 uC (micro)and -2 uC, respectively. What is the magnitude of the electric field at the midpoint between the two charges?
i think i know how to do it:
both E1 and E2 go in the same direction
E1=0.72 * 10^7 and E2 = 0.72 * 10^7
then you add
and you get
1.44 * 10^7
is that correct?
Where did you get .72 from?
To find the magnitude of the electric field at the midpoint between the two charges, you need to calculate the individual electric fields due to each charge and then add them together.
The formula to calculate the electric field created by a point charge is given by:
E = k * (Q / r^2)
Where:
E is the electric field
k is the Coulomb's constant (approximately equal to 9.0 x 10^9 Nm^2/C^2)
Q is the charge of the point charge
r is the distance from the point charge to the location where you want to calculate the electric field.
In your case, you have two charges: 2.0 uC (micro) and -2.0 uC, separated by 10.0 cm (0.10 m).
First, let's calculate the electric field created by the 2.0 uC charge at the midpoint:
Q1 = 2.0 uC = 2.0 x 10^-6 C
r1 = 0.10 m
Using the electric field formula, we can substitute the values:
E1 = (9.0 x 10^9 Nm^2/C^2) * (2.0 x 10^-6 C) / (0.10 m)^2
Simplifying the calculation gives:
E1 = 0.72 N/C
Similarly, let's calculate the electric field created by the -2.0 uC charge at the midpoint:
Q2 = -2.0 uC = -2.0 x 10^-6 C
r2 = 0.10 m
Using the formula again, we have:
E2 = (9.0 x 10^9 Nm^2/C^2) * (-2.0 x 10^-6 C) / (0.10 m)^2
Simplifying the calculation gives:
E2 = -0.72 N/C
Now, we add the electric fields E1 and E2 to find the total electric field at the midpoint:
E_total = E1 + E2
= 0.72 N/C + (-0.72 N/C)
= 0
Therefore, the magnitude of the electric field at the midpoint between the two charges is 0 N/C.