The conducting box in FIGURE EX24.26 has been given an excess negative charge. The surface density of excess electrons at the center of the top surface is . What are the electric field strengths to at points 1 to 3?
The electric field strengths are :
Given : The surface density at the center of the top surface is :
Theory used :
The electric field inside a conductor is zero at all times when it is in electrostatic equilibrium. However, all surplus charges on the conductor accumulate on the outside surface, and as further charges are added, they spread out on the outer surface until they reach the electrostatic equilibrium points.
The electric field at the surface of a charged conductor is given by the equation (1)
where is the surface charge density, which is a physical parameter that relies on the conductor's form.
Because the excess charge is expressed in , we must convert the surface charge density to using
There is an electric field at point 1, thus we apply
As previously stated, there is no electric field inside the wire, hence the electric field at point 2 is zero. That is .
Because all charges are concentrated at the outer surface at point 1, there are no net charges at point 3, and the electric field is zero. That is, .
A sphere of radius has total charge . The volume charge Calc density within the sphere is , where is a constant to be determined.
a. The charge within a small volume is . The integral of over the entire volume of the sphere is the total charge . Use this fact to determine the constant in terms of and .Hint: Let be a spherical shell of radius and thickness . What is the volume of such a shell?b. Use Gauss's law to find an expression for the electric field strength inside the sphere, , in terms of and .c. Does your expression have the expected value at the surface, ? Explain.
A tetrahedron has an equilateral triangle base with-long edges and three equilateral triangle sides. The base is parallel to the ground, and a vertical uniform electric field of strength passes upward through the tetrahedron. a. What is the electric flux through the base? b. What is the electric flux through each of the three sides?
| A spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball 1r … R2 is E1r2 = r4 Emax /R4 . a. What is Emax in terms of Q and R? b. Find an expression for the volume charge density inside the ball as a function of Verify that your charge density gives the total charge Q when integrated over the volume of the ball
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