f radius R has a homogeneous surface charge density . Determine the electric field at point P which lies along a line perpendicular to the center of the disk at a distance x from the center of the disk (see figure). Review the results obtained for the case R >> x
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A disk of radius R has a homogeneous surface charge density . Determine the electric field at point P which lies along a line perpendicular to the center of the disk at a distance x from the center of the disk (see figure). Review the results obtained for the case R >> x
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- Q. A disk of radius R has a uniform surface charge density o. Calculate the clectric ficld at a point P that lies along the central perpendicular axis of the disk and a distance x from the center of the diskvery long and thin insulating rod has a charge of +Q uniformly distributed along its length. The rod has a length L. Use Gauss’s lawto determine the electric field near the middle of the rod a short distance, d, from the axis of the rod.A charge of Q is distributed as a quarter circle of a radius R. Lambda(theta)= lambda 0 sin theta provides the linear charge density where theta = 0 degrees along the positive x-axis. How would you find the constant of lambda in terms of Q and R, and what would the magnitude of the electric field be equal to at the center point?
- A non-uniform electric field directed along the x-axis penetrates a cubical surface oriented as shown in the figure. The cube has an edge length of L=0.79 m and the field varies from E1=2000 N/C at x=0 to E2=5000 N/C at x=L. Find the total charge (in nC) enclosed by the cube.A line of charge of length L=29m with charge density λ=43.0μC/m lies along the positive Y-axis whose one end is at the origin O. A point charge q=42.0μC lies on the X-axis at (10,0,0) and point P lies on the Z-axis at 20m from the origin. Here the coordinates are given in meters. a) Find the electric field at P due to the line of charge only. (Hint: You may have to do an integration.) I) x-component II) y-component III) z-component b) Find the net electric field at point P I) x-component II) y-component III) z-component-->> R In the figure we see a rod of length LA = 22 cm carries a charge QA = 22 nC and a circular arc of radius RB = 13 cm caries a charge QB = 49 nC. The center of the rod is at y = 4 cm from the origin. a) Find the charge density for both the rod and the arc. charge density of the rod Give your answer up to at least three significance digits. C/m charge density of the arc Give your answer up to at least three significance digits. Activa C/m Go to S
- Find the electric field at the origin of the x,y-plane for charge distributions (a) and (b), see the figures shown below. The field is produced (a) by a thin half-circle with a radius of 15 cm and the linear charge density K-10 pc/cm and (b) by a thin quarter-circle with the same radius and the linear charge density K = -10 pc/cm. K>0 (a) For the charge distribution (a): The x-component of Ea. Ea,x= The y-component of Ea, Ea,y= For the charge distribution (b): The x-component of Eb, Eb,x- The y-component of Eb, Eb,y = Units N/C Units N/C Units N/C Units N/C K<0 (b)Electric Field IntegralsA solid sphere of radius 40.0 cm has a total positive charge of 24.8 μC uniformly distributed throughout its volume. Calculate the magnitude of the electric field at the following distances. (a) 0 cm from the center of the sphere X What would be the direction of this electric field at the origin? kN/C (b) 10.0 cm from the center of the sphere X How much charge is contained within a sphere of radius 10 cm? kN/C (c) 40.0 cm from the center of the sphere X How much of the total charge is contained within a sphere of radius 40 cm? kN/C (d) 62.5 cm from the center of the sphere X Would the field at this point be affected if the charge were moved to a point at the origin? kN/C
- There is a +5C charge at the center of a hollow sphere made of a perfect conductor. The hollow sphere has a net charge of +2C, an inner radius of 0.5 m and an outer radius of 0.75 m. Calculate the electric field as a function of distance from the +5C charge and the charge on each surface of the hollow sphere.A cube has positive charge +Q in all corners except for one, which has a negative point charge - Q. Let the distance from any corner to the center of the cube be r. What is the magnitude and direction of the of electric field at the center of the cube (point P)?Consider a spherical conducting shell of inner radius a=0.1 m and outer radius b= 0.15 m. The shell carries a net charge of Q= +49 nC. A point charge of -1 nC is placed at the center, as shown in the figure. Find the surface charge density (in nC/m2) on the outer surface of the shell. Conductor with a net charge + Q -1 nC a