Two positive charges of 5.43 µC each are
508 cm apart.
Find the electric field midway between
them.
What is the magnitude of the electric field if
one charge is positive and the other negative,
both of magnitude 5.43 µC?
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To find the electric field midway between two positive charges, we can use the formula for electric field due to a point charge:
E₁ = k * q₁ / r₁²
where E₁ is the electric field due to one charge, k is the Coulomb's constant (9 x 10^9 Nm²/C²), q₁ is the magnitude of the charge, and r₁ is the distance from the charge.
In this case, we have two positive charges of magnitude q₁ = 5.43 µC each, and they are separated by a distance r₁ = 508 cm.
To find the electric field midway between them, we need to find the electric field due to each charge at that point and then add them together.
First, let's convert the distance r₁ to meters:
r₁ = 508 cm = 508 x 0.01 m = 5.08 m
Now, substitute the values into the formula and calculate the electric field due to one charge:
E₁ = (9 x 10^9 Nm²/C²) * (5.43 x 10^(-6) C) / (5.08 m)²
E₁ = 4.51 x 10^4 N/C
Since we have two charges, one positive and the other negative, both of magnitude 5.43 µC, and they are equal in magnitude, the electric field due to the negative charge will have the same magnitude but opposite direction to the electric field due to the positive charge.
Therefore, the magnitude of the electric field at the midpoint between the charges will be:
E_total = E₁ - E₁ = 4.51 x 10^4 N/C - 4.51 x 10^4 N/C = 0 N/C
So, the magnitude of the electric field at the midpoint between the two charges, when one is positive and the other negative, both of magnitude 5.43 µC, is zero.