Two small insulating spheres with radius 7.00×10^−2m are separated by a large center-to-center distance of 0.565m . One sphere is negatively charged, with net charge -2.05μC , and the other sphere is positively charged, with net charge 4.10μC . The charge is uniformly distributed within the volume of each sphere.
What is the magnitude E of the electric field midway between the spheres?
Take the permittivity of free space to be ϵ0 = 8.85×10^−12C2/(N⋅m^2) .
Please provide answer
E=____N/C
thank you
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To find the magnitude of the electric field E at the midpoint between the spheres, we can use the principle of superposition. The electric field due to each sphere individually can be calculated using the formula:
E = (k * Q) / r^2
where E is the electric field, k is the electrostatic constant (k = 9 * 10^9 N m^2/C^2), Q is the charge, and r is the distance between the center of the sphere and the point where the electric field is to be calculated.
However, since the spheres have opposite charges, the electric fields due to each sphere will be in opposite directions. Therefore, to find the total electric field at the midpoint between the spheres, we need to subtract the magnitudes of the electric fields due to each sphere.
First, let's calculate the electric field due to the negatively charged sphere:
E_neg = (k * Q_neg) / r^2
= (9 * 10^9 N m^2/C^2) * (-2.05 * 10^-6 C) / (0.565/2)^2
Next, let's calculate the electric field due to the positively charged sphere:
E_pos = (k * Q_pos) / r^2
= (9 * 10^9 N m^2/C^2) * (4.10 * 10^-6 C) / (0.565/2)^2
Now, let's calculate the net electric field at the midpoint between the spheres:
E_net = E_pos - E_neg
Note that the midpoint is equidistant from the centers of both spheres, so the distance r is equal to the radius of each sphere, 7.00 * 10^-2 m.
Once you've plugged in the values and performed the calculations, you will find the magnitude of the electric field E at the midpoint between the spheres.