What is the electric field at a point midway between a -7.34 micro coulombs and a +4.49 micro coulombs charge apart 31.5m apart?

E=E₁+E₂=k|q₁|/(d/2)²+ k|q₂|/(d/2)²=

k/(d/2)²{ |q₁|+ q₂}=
=9•10⁹(7.34+4.49) •10⁻⁶/0.1575=
=6.76•10⁵V/m (directed to the negative charge)

To find the electric field at a point midway between two charges, you can use Coulomb's Law. Coulomb's Law states that the electric field created by a point charge is directly proportional to the product of the charge and inversely proportional to the square of the distance between the charges.

The formula for Coulomb's Law is:

E = k * (q1 * q2) / r^2

Where:
E is the electric field
k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
q1 and q2 are the magnitudes of the charges
r is the distance between the charges

In this case, you have two charges, q1 = -7.34 micro coulombs and q2 = +4.49 micro coulombs, and the distance between them, r, is 31.5m. Since the charges have different signs, the electric fields created by each charge will have opposite directions. Therefore, you will need to calculate the electric field created by each charge separately and then subtract their magnitudes to find the net electric field.

Let's calculate the electric field created by each charge:

For the first charge (q1 = -7.34 micro coulombs):
E1 = k * (q1 * q2) / r^2

Plugging in the values:
E1 = (9 x 10^9 Nm^2/C^2) * (-7.34 x 10^-6 C * 4.49 x 10^-6 C) / (31.5m)^2

Now, calculate the electric field created by the second charge (q2 = +4.49 micro coulombs) using the same formula:

E2 = (9 x 10^9 Nm^2/C^2) * (q1 * q2) / r^2

Plugging in the values:
E2 = (9 x 10^9 Nm^2/C^2) * (4.49 x 10^-6 C * 7.34 x 10^-6 C) / (31.5m)^2

Finally, subtract the magnitudes of the electric fields to find the net electric field:

E_net = |E1| - |E2|

Now, calculate the absolute value of each electric field magnitude and subtract them:

E_net = |E1| - |E2|

After performing all the calculations, you will have the net electric field at the point midway between the two charges.