Two uniform spherical charge distributions (see figure below) each have a total charge of 85.7 mC and radius R = 15.2 cm.Their center-to-center distance is 37.50 cm. Find the magnitude of the electric field at point A midwaybetween the two spheres.
N/C
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if A is on a line between the two centers, the field is zero
To find the magnitude of the electric field at point A, we can use the principle of superposition. According to this principle, the electric field at a point due to a system of charges is equal to the vector sum of the electric fields produced by each individual charge.
To calculate the electric field at point A, let's break the problem down into three steps:
Step 1: Determine the electric field due to each individual sphere at point A.
Step 2: Use the principle of superposition to find the net electric field at point A.
Step 3: Calculate the magnitude of the net electric field at point A.
Step 1: Determine the electric field due to each individual sphere at point A.
The electric field due to a uniformly charged sphere at a point on its axis is given by the equation:
E = k * Q / (R^2)
where E is the electric field, k is Coulomb's constant (9 × 10^9 Nm^2/C^2), Q is the charge of the sphere, and R is the radius of the sphere.
In this case, both spheres have the same charge (Q = 85.7 mC) and radius (R = 15.2 cm).
Calculating the electric field due to each sphere:
E1 = k * Q / (R^2)
E2 = k * Q / (R^2)
Step 2: Use the principle of superposition to find the net electric field at point A.
Since the two spheres are symmetrically placed with respect to point A, the electric fields they produce at A will have the same magnitude and will be pointing in opposite directions.
So, the net electric field at point A will be the difference between the electric fields due to the two spheres:
E_net = E1 - E2
Step 3: Calculate the magnitude of the net electric field at point A.
To find the magnitude of the net electric field at point A, we can use the equation:
|E_net| = |E1 - E2|
Now, let's plug in the values and calculate the magnitude of the net electric field at point A.