the front of the book has a legend for the gradient in spherical coordinates so i used that. the question was just worded weird.Simon Bridge said:By definition: ##\vec E = -\vec\nabla V## ... you will need ##\nabla## in spherical-polar coordinates.
Check how the equations in your book were derived - make sure you understand the reasoning involved. Then you can make a determination about how appropriate they are for your situation.
Then you have the answer to your first question - well done.nmsurobert said:the front of the book has a legend for the gradient in spherical coordinates so i used that. the question was just worded weird.
This is another odd wording I think. You seem quite good at figuring this stuff out...also, the question asks for "surface charge distribution of the sphere".
is that just the surface charge density?
The formula for calculating E_r (radial electric field) and E_θ (tangential electric field) for a grounded conducting sphere in a uniform electric field is:
E_r = -E_θ = -E₀cos(θ)
Where E₀ is the strength of the electric field and θ is the angle between the direction of the electric field and a point on the surface of the sphere.
In a grounded conducting sphere, the electric field will cause the charges to redistribute themselves on the surface of the sphere. The charges will accumulate on the side of the sphere closest to the source of the electric field, resulting in a non-uniform charge distribution.
The grounded condition means that the conducting sphere is connected to a conducting path that leads to the ground. This allows the sphere to maintain a constant potential and ensures that the electric field inside the sphere is zero. Without this condition, the electric field inside the sphere would be non-zero and the charges would not distribute themselves in the same way.
Yes, the formula can be used for any type of conducting sphere as long as it is in a uniform electric field and is grounded. The only difference between different types of conducting spheres may be the shape or size, which would affect the angle θ at different points on the surface.
The angle θ affects the distribution of charges as it determines the direction and magnitude of the electric field at different points on the surface of the sphere. At θ = 0 (directly facing the electric field), the charges will be evenly distributed, but as θ increases, the charges will accumulate on one side of the sphere.