A spherical shell of radius R carries a total charge Q. What is the electric fie

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Question: A spherical shell of radius R carries a total charge Q. What is the electric field at a point outside the shell?

Options:

Correct Answer: Q/(4πε₀R²)

Solution:

For a spherical shell, the electric field outside the shell behaves as if all the charge were concentrated at the center, so E = Q/(4πε₀R²).

A spherical shell of radius R carries a total charge Q. What is the electric field at a point outside the shell?

A spherical shell of radius R carries a total charge Q. What is the electric field at a point outside the shell?

Step 1: Understand that we have a spherical shell with a radius R and a total charge Q distributed on it.
Step 2: Recognize that we want to find the electric field at a point that is outside this spherical shell.
Step 3: Recall the principle of symmetry: for a spherical shell, the electric field outside behaves as if all the charge were concentrated at the center of the shell.
Step 4: Use the formula for the electric field due to a point charge, which is E = k * Q / r², where k = 1/(4πε₀) and r is the distance from the center to the point where we are measuring the electric field.
Step 5: In our case, since we are outside the shell, we can set r = R (the radius of the shell) for the electric field calculation.
Step 6: Substitute the values into the formula: E = Q / (4πε₀R²).
Step 7: Conclude that the electric field at a point outside the shell is given by E = Q / (4πε₀R²).

Gauss's Law – The electric field outside a uniformly charged spherical shell can be determined using Gauss's Law, which states that the electric field due to a symmetric charge distribution can be treated as if all the charge were concentrated at a point.
Electric Field of Spherical Shells – For a spherical shell, the electric field outside the shell is equivalent to that of a point charge located at the center of the shell.