مسائل فى الكهربيه 2

السلام عليكم ورحمه الله وبركاته انا قلت متاخرش فى طرح المسائل الباقيه علشان مجبرش حد انه يتابع معاى وخاصه انه انا داخل على امتحانات واتمنى انها تعجبكم ولسه مجموعه اخرى ان شاء الله

المجموعه الثالثه :


Given the electric vector D = (2x + 1)y2 ax + 2x(x + 1)y ay C/m2, compute the electric flux crossing the rectangular surface x = 5, -2 ≤ y ≤ 2, -2 ≤ z ≤ 2.

A uniform line charge of 15nC/m lies along the z axis and a uniform sheet of charge of 4 nC/m2 is located at the plane z = 1. What is the total electric flux leaving the sphere 2 = 2? What is the magnitude of the electric vector D at the point on the sphere where x = 2?

The spherical surfaces r = 3, 4, and 5 m contain uniform surface charge densities of 8, -12, and ρs nC/m2, respectively. What value must ρs be so that D = 0 for r > 5? If ρs = 2 nC/ m2., calculate and plot Dr vs. r for 0 ≤ r ≤ 6 m.

In spherical coordinates ρ = 4 nC/m3 for 0 ≤ r ≤ 2 cm, ρ = 32/ r3 pC/m3 for 2 ≤ r ≤ 4 cm, and ρ = 0 elsewhere. Select suitable gaussian surfaces, obtain expressions for Dr, and evaluate at r= 0,1,3, and 5 cm.

If D = [(20 cos 1/2 φ)/r] aφ in the region 1 ≤ r ≤ 2, 0 ≤ φ ≤ π, 0 ≤ z ≤ 2.5, determine the total charge lying within the given region by two different methods.

Within the cylindrical region r ≤ 5 m, the electric flux density is given as 4r2 ar C/m2. What is the volume charge density at r = 2? How much electric flux leaves the cylinder r = 2, -5 ≤ z ≤ 5? How much charge is contained within this cylinder?

Given that D = 30 e-r ar - 2z az in cylindrical coordinates, Evaluate both sides of Gauss law for the volume enclosed by r = 2, z = 0, and z = 5.

Volume charge of density ρ = k/r2 exists in the sherical region a ≤ r ≤ b. Use Gauss’ law and suitable gaussian surfaces to find the electric field E in the three regions r < a, a < r < b, and r > b.
An electric fieldis given as E = -10ey (sin 2z ax + x sin 2z ay + 2x cos 2z az) V/m. Find the magnitude E of the electric field at the point P(5,0, π/2). How much work is done in moving a charge of 2 C an incremental distance of 1 mm from point P in the direction: i- az ii- (2ax + 3ay - az)?
Given E = 10y ax + 10x ay - 2 az V/m, determine the work involved in carrying a charge of 3 C from (0,-2,8) to (5,3,23) along the path: i- z = 2x2 – y3, y2 = x + 4; ii- the straight line joining the two points.

Given E =[10/(x2 + y2) ] (x ax + y ay) - 2 az V/m. Let the potential be 10 V at the point (3,4,5). Find the potential at the point (6,-8,7).

Electric charge is distributed nonuniformly along the negative y axis in free space as ρL = 1/(y2 + 1) nC/m. Assuming the potential V = 0 at infinity, find V at the two points (0,1,0) and (1,0,0).



المجموعه الرابعه :


A conducting sphere of radius R has a total charge of Q C. Within what radius is 90 percent of its energy stored?

Two point charges +q and –q are placed at the points (0,0,d/2) and (0,0,-d/2), respectively. The charges form an electric dipole of moment P = Qd az. Show that the potential at a far poit (r,θ,φ) is V = P cos θ / (4πεor2), r >> d. Determine E at a far point in terms of P.

An air filled parallel plate capacitor is made of two perfectly conducting plates each of area A.. The plate seperation is d. The voltage between the plates is V. Find the force acting on each plate

A parallel plate capacitor is made of two perfectly conducting square plates 500 mm on a side seperated by 10 mm. A slab of sulfur of relative dielectric constant εr = 4 and thickness 6 mm is placed on the lower plate, leaving an air gap of 4 mm thick between it and the upper plate. If the lower plate is at 0 voltage and the upper one at voltage V, find the electric field E in each region, the charge density on each plate, and the capacitance between them. Neglect fringing of the fields at the edges.

A conducting sphere of radius R has a total charge of Q C. What is the force of repulsion between the "northern" hemisphere and the "southern" hemisphere?

A spherical region of space of radius a contains a charge Q distributed uniformly with constant volume charge density ρ. Determine the stored electrostatic energy. Compare it to the energy of two point charges Q that are seperated by a distance a.

A solid conducting sphere of radius R has a total charge of Q C. The solid sphere is surrounded by a thick concentric ****l ****l of inner radius a and outer radius b. The ****l carries no charge.
(a) Find the surface charge density on the surfaces r = R, r = a, and r = b.
(b) Find the potential at the center using infinity as reference, i.e. assuming the potential =0 at infinity.
(c) If the outer surface r = b is touched to a grounding wire which lowers its potential to zero, how do your answers to (a) and (b) change?

8- Two spherical cavities, of radii a and b, are hollowed out from the interior of a neutral perfectly conducting solid sphere of radius R. At the center of each cavity a point charge is placed: call these charges qa and qb
(a)Find the suface charges on the inner surfaces of the cavities and the outer surface of the sphere..
(b)What is the field outside the conductor?
(c)What is the field within each cavity?
(d)What is the force on qa and qb?
(e)Which of these answers would change if a third charge q is brought near the conductor?


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