(1) The goal of this problem is to find the electric field inside of a cavity which is cut into a uniformly charged solid cylinder with infinite length. Inside of the cavity, there is no net charge, but this cavity is off-center. To do this, we will consider it as a solid, uniformly positively charged cylinder (with no cavity) added to a solid, uniformly negatively charged cylinder such that +
ho _(0)-
ho _(0)=0 in the space where the two cylinders coexist ^(1). But in order to add the two fields in this case, the fields have to be calculated from the same origin (see part (c) for more on that). This may sound strange, but imagine a solid object where we've just ionized a bunch of atoms such that most of the material is positively charged. But we leave the electrons in a small cylindrical region off-center. This is equivalent to having a solid cylinder of ALL ions where we then insert a cylinder of electrons to make that section neutral atoms.
(a) Find the electric field inside of a solid cylinder with uniform charge density,
ho _(0), which is located at the origin.
(b) Find the electric field inside of a solid cylinder with uniform charge density, -
ho _(0), which is located at the origin.
(c) If we shift the negatively charged cylinder from part (b) to be centered at a position vec(p) rather than the origin, what is the location of a random point inside of your negatively charged cylinder as measured from the origin (vec(r)) ? Express this answer in terms of the location of the center of the negatively charged cylinder (vec(p)) and the location of the random point measured from the center of the negative sphere (vec(r)^('))*.^(2)
(d) Use parts (a), (b), and (c) to find the electric field inside of a neutral cavity in an otherwise uniformly charged, cylinder.
(e) Find the electric field of this cylinder with the cavity outside the cylinder, at a point P which located a distance a from the axis of the cylinder. The vector from the center of the cylinder to point P(vec(a)) is parallel to vec(p).
Please complete all parts thank you!!.
(1) The goal of this problem is to find the electric field inside of a cavity which is cut into a uniformly charged solid cylinder with infinite length. Inside of the cavity, there is no net charge, but this cavity is off-center.To do this,we will consider it as a solid,uniformly positively charged cylinder (with no cavity added to a solid, uniformly negatively charged cylinder such that +o - Po - 0 in the space where the two cylinders coexist But in order to add the two fields in this case,the fields have to be calculated from the same origin (see part c for more on that.This may sound strange,but imagine a solid object where we've just ionized a bunch of atoms such that most of the material is positively charged. But we leave the electrons in a small cylindrical region off-center. This is equivalent to having a solid cylinder of ALL ions where we then insert a cylinder of electrons to make that section neutral atoms. a Find the electric field inside of a solid cylinder with uniform charge density,Po,which is located at the origin (b) Find the electric field inside of a solid cylinder with uniform charge density,-Po, which is located at the origin. c If we shift the negatively charged cylinder from part(b) to be centered at a position p rather than the origin, what is the location of a random point inside of your negatively charged cylinder as measured from the origin r? Express this answer in terms of the location of the center of the negatively charged cylinder (p and the location of the random point measured from the center of the negative sphere (r d Use parts (a),(b), and (c to find the electric field inside of a neutral cavity in an otherwise uniformly charged, cylinder (e) Find the electric field of this cylinder with the cavity outside the cylinder, at a point P which located a distance a from the axis of the cylinder.The vector from the center of the cylinder to point Pis parallel to p.
