Electric Field

For a charged metallic sphere, the electric field at a distance from the center of the sphere, where , behaves as if the entire charge is concentrated at the center of the sphere. This is a consequence of the spherical symmetry of the charge distribution, and we can apply Coulomb's law to calculate the electric field. Step 1: Potential on the Surface of the Sphere.
The potential at the surface of the sphere is related to the charge on the sphere and the radius of the sphere by the formula: where: is the total charge on the sphere, is the radius of the sphere, is the permittivity of free space. Rearranging the equation for , we get: Step 2: Electric Field Outside the Sphere.
Now, we need to calculate the electric field at a distance from the center of the sphere, where . According to Coulomb's law, the electric field at a distance from a point charge is given by: Substituting the expression for from Step 1: Step 3: Simplifying the Expression.
Simplifying the equation: Thus, the magnitude of the electric field at a distance from the center of the sphere is: Therefore, the correct answer is .

We are given a charge placed in an electric field of intensity , and we need to find the force experienced by the charge. Step 1: Use the formula for the force in an electric field The force experienced by a charge in an electric field is given by the formula: Where: - is the force, - is the electric field intensity, - is the charge. Step 2: Substitute the known values Substitute and into the formula: Step 3: Conclusion The force experienced by the charge is . Answer: The force experienced by the charge is , so the correct answer is option (1).