1.) Consider a very long, straight wire of uniform positive charge density. In the space below, describe the electric field of the wire. In particular, what direction does it point? Does its strength depend on position? If so, how? Note any symmetries of interest.
2.) Use the understanding of electric fields you developed above to deduce the electric field at the center of a circular loop of wire (radius R) with the same positive uniform charge density. Specifically, is it:
Zero
The same magnitude as the electric field a distance R from a straight wire
Larger than the electric field a distance R from a straight wire
Smaller than the electric field a distance R from a straight wire
3.) Explain how you arrived at your answer. Qualitative arguments are encouraged.
1.) Consider a very long, straight wire of uniform positive charge density. In the space below,...
1.) Consider a very long, straight wire of uniform positive charge density. In the space below, describe the electric field of the wire. In particular, what direction does it point? Does its strength depend on position? If so, how? Note any symmetries of interest. 2.) Use the understanding of electric fields you developed above to deduce the electric field at the center of a circular loop of wire (radius R) with the same positive uniform charge density. Specifically, is it:...
You will explore the electric fields of charged wires and circular loops and the fields of current-carrying versions of these same objects, so this question is meant to give you a reference point with which to compare and contrast the two types of fields. 1. Consider a very long, straight wire of uniform positive charge density. In the space below, describe the electric field of the wire. In particular, what direction does it point? Does its strength depend on position?...
An infinitely long straight wire has a uniform linear charge density of λ. Derive the equation for the electric field a distance R away from the wire using Gauss's Law for Electrostatics.
An infinitely long straight wire is uniformly charged with a positive linear charge density +?. It is surrounded by an insulating hollow cylinder (also infinitely long) of inner radius R and outer radius 2R. The hollow cylinder has a uniform charge density ?. (a) Determine the value of ? if the electric field vanishes at every point outside the cylinder (r > 2R). (b) Determine the electric field in the region 0 < r < R. (c) Determine the electric...
Question: Consider one infinitely long straight wire with a uniform charge density of 1C/m. Sketch the electric field around the wire Question: In the above problem, calculate the magnitude of the electric field at a distance R from the wire. How is it different (if any)from the field of a point charge? Question: Consider two infinite wires 1 m apart with a uniform charge density per unit length 1 C/m. Calculate the force per unit length between the wires. To...
Consider an infinitely long straight cylinder of radius R and uniform positive charge density ρ. (a) Find the field inside the cylinder a distance r < R from the center. (b) Find the field outside the cylinder a distance r > R from the center. (c) Sketch a plot of E vs r over the range 0 ≤ r ≤ 2R.
An infinitely long, straight, cylindrical wire of radius R carries a uniform current density J. Using symmetry and Ampere's law, find the magnitude and direction of the magnetic field at a point inside the wire. For the purposes of this problem, use a cylindrical coordinate system with the current in the +z-direction, as shown coming out of the screen in the top illustration. The radial r-coordinate of each point is the distance to the central axis of the wire, and...
4. An infinitely long, thin wire contains a uniform charge density +λo and is oriented along the z-axis. Assume that the potential at s = 0 is zero. a) Find an expression for the electric field for the wire in Cartesian coordinates and convert it to cylindrical coordinates. b) Use your answer from (a) to solve for an expression for the electric potential at a distance s from the wire. Use cylindrical coordinates for this. c) Now solve for an...
A long straight wire has fixed negative charge with a linear charge density of magnitude 3.2 nC/m. The wire is to be enclosed by a coaxial, thin-walled, nonconducting cylindrical shell of radius 2.0 cm. The shell is to have positive charge on its outside surface with a surface charge density σ that makes the net external electric field is zero. Calculate σ.
Consider a long, cylindrical charge distribution of radius R with a uniform charge density ?. Find the electric field at distance r from the axis, where r < R. (Use any variable or symbol stated above along with the following as necessary: ?0.)