-2n de The value of the integral I = o 2+cos 0 2n V3 V3

The electric potential of a charged conducting sphere (as well as a spherical shell) can be calculated as Q R' V = k where is the charge and R is the radius of the sphere. Calculate the electric potential of a solid conducting sphere of a radius of R = 6 cm if the sphere loses 0.1% from the total number of its free electrons. The sphere is made of aluminum and has the density 2.7 g/cm³, molar mass 27 g/mol and one free electron per atom. Follow the steps listed below. 1. Find the number of free electrons per cm³ in aluminum. The number of free electrons per cm³, ne = Units Select an answer ✓ 2. Calculate the volume of the sphere and use it to find the total number of free electron inside the sphere. The number of free electrons, Ne = Units Select an answer 3. Calculate the charge of the sphere after it loses 0.1% of its electrons and use it to find the potential of the sphere. The electric potential of the sphere, V = Units Select an answer ✓

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

fig 5 Me= In Figure 5. the electron on the right side is fixed. and the one on the left side has initial velocity 10' m/s towards the first electron at the distance shown. Determine the final speed of the mobile electron when it is far away from the fixed one.

A charged conducting spherical shell of radius R = 3 m with total charge q = 23 μC produces the electric field given by E⃗ (r)={014πϵ0qr2r̂ forforr<Rr>R(PICTURE ATTACHED OF EQUATION) a. Enter an expression for the electric potential inside the sphere ( r < R ) in terms of the given quantities, assuming the potential is zero at infinity.  V(r)= b. Calculate the electric potential, in volts, at radius r inside the charged shell. V(r) =

A charge Q field E and the electrostatic potential at rı 10-10C is uniformly distributed on a sphere of radius R= 10cm. What is the valued of the electric R. , r2 = R, r3 = 2R from the center of the sphere?

Electrons are accelerated through a potential difference, Vo = 120 V, before exiting and being subjected to a new set of parallel plates. The electrons enter this region 5.0 cm from the bottom plate, and hit this bottom plate a distance of 5.0 cm in. If the total plate separation of this second set of plates is 8.0 cm, determine the voltage of the second source AND draw this source in, clearly showing the positive vs negative terminals of the battery. (m= 9.11 x10-³¹kg, q = -1.6x10-¹⁹℃) T P Vo Yo Yo D

Answers: a) 3.3 C c/m² 6. Two electrons are fixed 2.00 cm apart. Another electron is shot from infinity and comes to rest midway between the two. What was its initial speed? Answer: 318 m/s

10. Metal tube of infinite length and square cross-section with sides 0 ≤x≤L, 0 ≤ y ≤ L has three of its sides at potential zero and the fourth (y=L) in potential U. It is requested to determine the potential at inside the tube. Assume that along the contact lines of between surfaces with different potential there is a thin insulating material.

In a certain region of space, the electric potential is V(z,9,2) = Czy – Ar + By %3D where A, B and C are positive constants. Calculate the r, y and z components of the electric fiekd.