he electrostatic potential in all space is given here as a function of x, y and z. Find the electric field E(x,y,z) function and express your answer using unit vectors. 1 V(x,y,z)=- %3D ²+y° +(z-d)° 4πεο .2

A capacitor is attached to a battery. It has initial capacitance Co, voltage Vo, charge Qo, and energy Uo. Let's put some dielectric material of dielectric constant K in there in two different ways. For each case, figure out the following for the resulting "new" capacitor: C, V, Q, and U, in terms of the old value and K. The capacitor is left attached to the battery. A slab of dielectric material with K=3 is inserted into the capacitor without otherwise disturbing it. In terms of the initial values, what are the new values? The capacitor is disconnected from the battery after it is charged up to Qo. Then, a slab of dielectric material with K=3 is inserted into the capacitor without anybody touching the plates or otherwise disturbing the capacitor. In terms of the initial values, what are the new values?

Consider a cube of side a with 8 charges (4 with charge +e and 4 with charge -e) at the 8 corners. a Since there are a total of 8 charges, there are 28 pars. This may seem like a lot of terms to add, but many of the terms are identical. For example, 12 of the pairs are of opposite sign and separated by an edge of the cube (a distance a). Also, 12 of the pairs are of the same sign and separated by a diagonal of one face (a distance √2 a). Finally, 4 of the pairs are of opposite sign and separated by a diagonal of the cube (a distance √3 a). Calculate the total electrostatic potential energy of this configuration by summing over all the pairs of charges. Give your answer as the numerical coefficient of the following expression U= 4²4 Give your answer to 4 significant figures, and make sure you include the proper sign.

O [HW3.1] A solid metal ball (radius a) is grounded inside a floating (isolated) metal sphere (inner radius b, outer radius d). The sphere comes with total charge Q. Find surface charge density on every surface (the outer surface of the metal ball, inner and outer surface of the sphere), and capacitance of the system.

Electric force and coulomb balance1. By considering this assembly as being infinite plane plates uniformly loaded with the same load in absolute values, but of opposite signs; obtain a relation giving the electric field (Etot) between the plates as a function of the potential difference (delta V) between them and the distance (d) which separates the plates.2. Write the (simple) expression of the electric force on the movable plate having a charge Qmobile immersed in the electric field generated by the fixed plate (Efixe), see image on the left.3. From the notions of uniformly charged infinite flat plates, determine a relation giving the value of the charge of the movable plate (Qmobile) from the electric field (Emobile) that it generates.4. Substitute the relation obtained in #3 into the electric force relation from #2 and use the electric field relation from #1 to obtain an equation of electric force as a function of potential difference (delta V), knowing that Emovable = EFixed.5.…

The uniform electric field E in the air outside the plane boundary of an LIH dielectric material is at an angle of 30° to the normal to the The relative permittivity & of the dielectric is 3.0. Find the angle that the electric field in the dielectric makes with the normal. Clearly state any boundary conditions that you boundary, as shown in Figure 2. use. 30° Eair air dielectric € = 3.0

Two 0.01 m radius spherical +1.0 µC uniform charge distributions are placed 0.2 m apart. How much electrical energy is contained in this system? It requires energy to form each of the spherical charge distributions as well as bring the two spheres together. Let us call the energy required to form the spherical charge distribution Wformation: Let us call the energy required to assemble or bring together the charges Wassembly: So, Wtotal = 2 x Wfor Formation + Wassembly The energy Wformation (in Joules) can be calculated as follows: 3 Q? Wformation 5 4πεα Where Q is the total charge of the sphere in Coulombs and a is the radius of the sphere in

The picture on the right shows a plate capacitor. You may assume that the two plates are very large compared to the separation between the plates (i.e. you may treat them as 'infinite' planes). The plates are charged to ±Q, each plate has an area of A, and the plates are separated by a distance d. The x-axis in this problem is pointing from the negative to the positive plate, with the origin at the negative plate. The electric field at point 2 has a magnitude of E. E=3000 A=1 m² d = 8 mm c. What is the electric field strength at point 1? d. What is the charge Q on the plates? ·area A IT +Q €0=8.85 x 10-12 -a X=0 e. What is the electric field strength at point 3? Part A: a. In the picture, sketch the electric field between the plates by drawing the field lines. b. Find the surface charge density n on each plate. Nm² 12 x(mm)

answer parts c and d

A positive charge q is fixed at point (3,4) and a negative charge −q is fixed at point (3,0). Determine the net electric force F→net acting on a negative test charge −Q at the origin (0,0) in terms of the given quantities and physical constants, including the permittivity of free space ε0. Express the force using ij unit vector notation. Enter precise fractions rather than entering their approximate numerical values.