A surface charge density is on a long straight metallic with a radius of a. (a) What is the voltage ∆V(r) inside and outside the pipe, relative to its surface? Hint: use the integral form of potential difference, ∆V = ∫E•dl. (b) Sketch a plot of the voltage for 0 < r < 5a.

Let z 0 is region 2 with &r2 = 7.5. Given that E₁ = 60ax − 100a, + 40a, V/m, Calculate D₂. (Hint: Boundary conditions)

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?

A parrallel plate capacitor has circular cross-section with a radius R and has a charge that varias Q(t). Take the spacing between the plates to be small so that you can assume the electric field is uniform for r < R and vanishes for r>R. Answer in terms of Q(t) and its derivatives.(a) What is the magnitude of the electric field inside the capacitor as a function of time? (b) Inside the capacitor (for r<R), what is the magnetic field as a fucntion of time at a distance r from the center? Use Ampere-Maxwel law with displacement current.

A parrallel plate capacitor has circular cross-section with a radius R and has a charge that varias Q(t). Take the spacing between the plates to be small so that you can assume the electric field is uniform for r < R and vanishes for r>R. Answer in terms of Q(t) and its derivatives.(a) What is the magnitude of the electric field inside the capacitor as a function of time? (E(t), find the surface charge density to find the electric field) (b) Inside the capacitor (for r<R), what is the magnetic field as a fucntion of time at a distance r from the center? Use Ampere-Maxwel law with displacement current. E(t) is uniform inside and zero outside.

If the magnitude of the electric field in air exceeds roughly 3 x 106 N/C, the air breaks down and a spark forms. For a two-disk capacitor of radius 26 cm with a gap of 1 mm, what is the maximum charge (plus and minus) that can be placed on the disks without a spark forming (which would permit charge to flow from one disk to the other)? i C

A region has a uniform electric field of 50 V/m up.  Point B is 3 meter to the left, and 4 meters above, point A.  The voltage at point A is 600 V.  What is the voltage at point B?

The voltage across a membrane forming a cell wall is 77.7 mV and the membrane is 9.02 nm thick. What is the electric field strength? (The value is surprisingly large, but correct.) You may assume a uniform E-field.

A dielectric rod with cross-section area of A and polarization of Px = ax² + b is extended from x = 0 to x = L. (a) Calculate the bound volume charge density and bound surface charge density. b) Determine the total bound charge.

Problem 5: Consider a parallel plate capacitor having plates of area 1.5 cm? that are separated by 0.028 mm of neoprene rubber. You may assume the rubber has a dielectric constant K = 6.7. Part (a) What is the capacitance in nanofarads? C = nF sin() cos() tan() 8 9 HOME cotan() asin() acos() E 4 5 6 atan() acotan() sinh() 1|2 |3 cosh() tanh() cotanh() +- END ODegrees O Radians Vol BACKSPACE DEL CLEAR Part (b) What charge, in coulombs, does the capacitor hold when 9.00 V is applied across it?