Electrostatics

The electric field inside a sphere with a given charge density is determined using the formula: For a spherical charge distribution, the electric field is expressed as: Given the charge density , substituting this into the equation yields: To calculate the enclosed charge : The electric field becomes zero when : Thus, the distance from the center of the sphere where the electric field goes to zero is .

Inside the Inner Shell Inside a uniformly charged shell, the electrostatic potential is constant. Since the inner shell has a charge and the outer shell has a charge , and given the spherical symmetry, the potential inside the inner shell is:$ r_1 \leq r < r_2 (+Q) -Q r Q r_i r \geq r_i \frac{k Q}{r_2} \frac{k Q}{r} \frac{1}{r} r=r_2 \frac{k Q}{r}=\frac{k Q}{r_2}$$ r \geq r_2 r \geq r_2 +Q -Q $

The infinite cylinder with a spherical cavity can be considered the superposition of an infinite cylinder and sphere of charge density . From the principle of superposition, we have the following:$ k=\frac{1}{4 \pi \epsilon_0}$ linear charge density$ $$ $$ $$ x=0$, but we know that the electric field would be 0 at the center

The problem involves determining the electric flux through a spherical surface of radius , centered on a point on a charged sphere's surface. To solve this, consider:The larger sphere of radius completely encloses the original charged sphere of radius .The enclosed charge can be found using the charge density and the volume of the initial sphere.The formula for electric flux is given by Gauss's law: The expression for the charge density is: Solving for , we get: Substituting into the expression for , we have: Thus, the electric flux through the spherical surface is:

The force on particle due to particle and the force on particle B due to particle are action-reaction pairs. According to Newton's third law of motion, these forces are equal in magnitude and opposite in direction.OrYou can also use Coulomb's law and you will find the magnitude to be the same, and for directions, you can see they are both positively charged and will move in the opposite direction from each other.

$ F F=m a, a=\frac{F_{\text {net }}}{m}$