Two point charges are separated by 10.0 cm and have charges of 2.0 μC and -2 μC, respectively. What is the electric field at the point midway between the two charges? (k = 8.99 x 109 N.m2/C2)
A. 28.8 x 10 6
B. 14.4 x 106
C. 7.19 x 106
D. 3.59 x 106
E. zero
i am getting D...but i got that wrong i don't know how to solve it
The answer is 1440 N/C
I got D. was that right?
To find the electric field at the point midway between two point charges, you can use the principle of superposition.
First, let's find the electric field due to each charge separately at the midway point. The electric field due to a point charge is given by the equation:
E = k*q / r^2
where E is the electric field, k is the Coulomb's constant (k = 8.99 x 10^9 N.m^2/C^2), q is the charge, and r is the distance from the charge.
For the positive charge of 2.0 μC, the distance from the charge to the midway point is half of the total separation between charges, which is 10.0 cm / 2 = 5.0 cm = 0.05 m.
Using the above formula, the electric field due to the positive charge at the midway point is:
E1 = (8.99 x 10^9 N.m^2/C^2) * (2.0 x 10^-6 C) / (0.05 m)^2
Evaluating this expression, we find:
E1 = 7.19 x 10^6 N/C
Similarly, for the negative charge of -2 μC, the electric field at the midway point is also 7.19 x 10^6 N/C, but directed in the opposite direction.
Since electric fields are vector quantities, to find the total electric field at the midway point, we need to add these two electric fields together.
The sum of the two electric fields is:
E_total = E1 + E2 = (7.19 x 10^6 N/C) + (-7.19 x 10^6 N/C) = 0 N/C
So, the electric field at the point midway between the two charges is zero.
Therefore, the correct option is E) zero.