A spherical shell of radius R carries a total charge Q. What is the electric field at a point outside the shell?
Practice Questions
1 question
Q1
A spherical shell of radius R carries a total charge Q. What is the electric field at a point outside the shell?
0
Q/(4πε₀R²)
Q/(4πε₀R)
Q/(4πε₀R³)
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).
Questions & Step-by-step Solutions
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Q
Q: A spherical shell of radius R carries a total charge Q. What is the electric field at a point outside the shell?
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).
Steps: 7
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).
