A solid spherical conductor has a net charge +Q on it at electrostatic equilibrium. a) Apply Gauss' law to find E as a function of r outside of the conductor (for r>R). b) Apply Gauss' law to find E inside of the conductor. c) Use your results from above to sketch E as a function of r R
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- Q: A long thin wire carrying a uniform line charge density +λ runs down the center of a long cylindrical tube of radius R carrying a line charge density -2λ distributed uniformly over its surface. Find expressions for the electric field as a function of radial distance r from the axis of the wire for (a) r<R and (b) r>R. Use a minus sign to indicate a field pointing inward. In this question would area, A=2πrL where L is the length of the wire and why is that?An infinite, uniform, line of charge is on the x-axis. The linear charge density is (lambda), with units of C/m. Find an expression for the electric field at a particular y-value on the y-axis at x=0, using Gauss's Law. Do this problem as if (lambda) is positive -- the answer is valid regardless of the sign. a. Which direction does the electric field point in, at the point. b. Suppose you moved the problem left or right, or rotated the problem about the x-axis. How does the problem change? c. Pick a shape for your Gaussian surface. Since you don't know the value (or expression) for E, you must pick a surface where the electric flux is either EA or zero. (E must be uniform over the surface for EA.) d. Write your expression for the flux, and your expression for the charge inside the surface. e. Solve the Gauss's Law equation for E. f. If (lambda) = 2.5 nC/m, and y = 8 cm, calculate the electric field. g. If a proton is at the point, calculate the force on the proton and its acceleration.A metal ball (electrically conductive) with a radius of R = 10cm was placed in a vacuum and charged with a positive charge Q = 20μC. Using Gauss's law, determine the function describing the value of the radial component of the electric field intensity vector depending on the distance from the center of the spherical field for distances greater than or less than the radius of the sphere. Sketch the course of this function describing on the XY axes the characteristic values for the distance equal to the radius of the sphere at the center of the sphere.
- A uniform volume charge distribution ρv=5 (nC/m3) exists in a sphere that has a radius of a=3 cm. What is the magnitude of the electric field intensity at a distance R=4 cm? (Use Gauss’s Law)A thin spherical shell of radius R1, carries a total charge Q1 that is uni-formly distributed on its surface. A second, larger concentric thin shell ofradius R2 carries a charge Q2 also uniformly distributed over the surface ofthe shell. Use Gauss’ law to find the electric field in the regions. (a) r< R1,(b) R1 <r < R2. and(ce) R2 <r. The electric charges are such that Q1 > 0 and the electric field is zero forr > R2. Find the ratio Q1 /Q2.Figure 2 shows a nonconducting rod with a uniformly distributed charge Q. The rod forms a half-circle with radius R and produces an electric field of magnitude Earc at its center of curvature P. If the arc is collapsed to a point at distance R from P, by what factor is the magnitude of the electric field at P multiplied?
- An infinite, uniform, line of charge is on the x-axis. The linear charge density is (lambda), with units of C/m. Find an expression for the electric field at a particular y-value on the y-axis at x=0, using Gauss's Law. Do this problem as if (lambda) is positive -- the answer is valid regardless of the sign. d. Write your expression for the flux, and your expression for the charge inside the surface. e. Solve the Gauss's Law equation for E. f. If (lambda) = 2.5 nC/m, and y = 8 cm, calculate the electric field. g. If a proton is at the point, calculate the force on the proton and its acceleration.A solid, insulating sphere of radius a shown in figure has a total charge -2Q . Concentric with this sphere is a conducting hollow sphere with a total charge 3Q whose inner and outer radii are b and c, as shown in Figure. a) Using Gauss Law find the magnitude of electrical field in the region r>c. The Gaussian surfaces used should be shown on the figure.The steps followed while applying Gauss's law should be written in detail.Charge is distributed uniformly over the plane ? = −5 cm with a surface charge density of 1/36? nC/m2. Find the Electric field intensity. Please provide a clear and understanable solutions and answer! Tysm!
- An infinite, uniform, line of charge is on the x-axis. The linear charge density is (lambda), with units of C/m. Find an expression for the electric field at aparticular y-value on the y-axis at x=0, using Gauss's Law. Do this problem asif (lambda) is positive -- the answer is valid regardless of the sign. d. Write your expression for the flux, and your expression for the charge inside the surface.If the surface charge density on the surface of a conductor, σ = (786 – X) mC/m2 , (where X is your Roll No.). Apply Gauss’ Law to find (with complete logical an mathematical justification): the normal (perpendicular) component of the Electric Field exactly above and below the boundary of the surface if the conductor is placed in free space.The electric field at 2 cm from the center of long copper rod of radius 1 cm has a magnitude 3 N/C and directed outward from the axis of the rod. (a) How much charge per unit length exists on the copper rod? (b) Whatwould be the electric flux through a cube of side 5 cm situated such that the rod passes through opposite sides of the cube perpendicularly?