A spherically symmetrical load distribution, however not uniform, has a density ρ(r) given by: ρ(r) = ρ0(1-r/R), for r≤R,            0,             for r≤R where ρ0 = 3Q/πR3 it is a positive constant. (a) Show that the total load contained in the distribution is equal to Q. (b) Show that the electric field in the region r≥R is identical to the electrical component produced by a point charge Q, located at r = 0. (c) Obtain an expression for the electric field in region r≤R. (d) Graph the electric field module E as a function of r.

Q: As shown in the figure below, a solid insulating sphere of radius a - 5.00 cm carries a net positive…

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Q: A spherical conducting shell has a radius R and a uniform surface charge density o. The ratio of the…

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Q: A solid insulating sphere of radius R has a volume charge density given by p= poexp(-r/a*), where…

A: We know that for a solid sphere with varying charge density is given by:- E= (∫ρ(r)r2dr) × 1/r2εo.…

Q: An electric field given by E:= 4.0iˆ + 3.0(y2 - 2.0)jpierces a Gaussian cube of edge length 2.0 mand…

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Q: A long coaxial cable is shown in the figure where the radii of the conducting concentric cylinders…

A: Recall  Gauss's law ∮E→.dA→=Q/ε0

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A: Every charge disturbs space in its vicinity creating what we call the electric field. This electric…

Q: An electric field Ē = axî + By txzk exists, in space where.a, B.Y are constant. Electric flux…

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Q: A long non-conducting cylindrical shell with inner radius a = 5.0 cm and outer radius b = 10.0 cm…

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Q: The electric field in terms of spherical coordinates is defined as follows: E = kr'r Here, k is the…

A: The charge density is dependent on the divergence of the electric field and the equation can be…

Q: The electric field on the surface of an irregularly shaped conductor varies from 56.0 kN/C to 28.0…

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Q: The electric field intensity in a region is E = 3x2zax + 2xyay - yz2az N/C. Determine the charge…

A: Charge density can be linear, surface, or volume in nature. A linear charge density is defined as…

Q: A solid ball of radius R has a uniform volume charge density and produces a certain electric field…

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Q: A solid conducting sphere, which has a charge Q1 =52Q  and radius  ra = 2.6R is placed inside a very…

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Q: 31 SSM ILW wwW In Fig. 22-54, a nonconducting rod of length L= 8.15 cm has a charge -q- -4.23 fC…

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Q: A spherical ball of charged particles has a uniform charge density. In terms of the ball’s radius R,…

A: The field maximum occurs at the outer surface. We have to find the value of the radius such that the…

Q: A uniform volume charge distribution ρv=5 (nC/m3) exists in a sphere that has a radius of a=3 cm.…

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Q: A circular ring of radius r of fine wire carries a uniformly distributed positive charge q. The…

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Q: The charge density of a non-uniformly charged sphere of radius 1.0 m is given as: For rs1.0 m; p(r)=…

A: Given, Charge density,ρ=ρ0(1-4r3) Radius,R=1 m

Q: O given the electrical flux density equal to (20r²a, 2), find m2- (i) The total electric flux…

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Q: A spherical conducting shell has a radius R and a uniform surface charge density o. The ratio of the…

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Q: A solid cylindrical conductor of radius a is surrounded by a concentric cylindrical shell of inner…

A: Given data The radius of the solid cylindrical conductor is a The inner radius of the concentric…

Q: Calculate the magnitude of the electric field on the perpendicular bisector of a uniformly charged…

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Q: A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it,…

A: radius of cylinder = Rvolume charge density = ρobservation point = r

Q: consider a spherical shell with inner radius R1=0.40m and outer radius R2=1.1m. the hollow insider…

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Q: In the YZ plane as shown in the figure, a ring with a properly charged R radius has a total Q load…

A: Electric field due to uniformly charged ring at axial point P which is h= 2R distance from the…

Q: Two infinite, uniformly charged, flat surfaces are mutually perpendicular. One of the sheets has a…

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Q: A charge +Q is distributed uniformly within a solid sphere of radius r, . It is surrounded by…

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Q: An infinitesimally thin, uniformly charged wire with longitudinal charge density A is given the…

A: Total charge on the wire = Q =λ×(L+2L+L+2L) =6λL Electric field due to circular ring of radius R and…

Q: Figure 22-32 shows two harged particles on an x axis: -q = --3.20 x 10-19 C at x = -3.00 m and g=…

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Q: A solid conducting sphere of radius R has a uniform charge distribution, with a density = Ps * r / R…

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Q: E, = bx? Let the distribution of electric field strength in a certain area of space be y E, = E. = 0…

A: Given,

Q: The charge density of a non-uniformly charged sphere of radius 1.0 m is given as: For rs 1.0 m;…

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Q: dx P. + + + + + + t + dq Evaluate an expression for the electric field at point P of a uniformly…

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Q: An electric fieldĒ =aî+Bj +yk exists in space, where a, B. y are constants. Magnitude of electric…

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Q: Given a 3.00 mm radius solid wire centered on the z-axis with an evenly distributed 2.00 coulombs of…

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Q: A segment of a hollow cylinders of height (L) with inner radius (a) and outer radius (b) is filled…

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Q: We have calculated the electric field due to a uniformly charged disk of radius R, along its axis.…

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Q: Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m. The…

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Q: A circular rod has a radius of curvature R = 9.00 cm and a uniformly distributed positive charge Q =…

A: The magnitude of electric field here can be given as We know,

Q: A solid metal cylinder of radius r = 1.9 cm is located coaxially inside a hollow metal cylinder of…

A: a) Applying the gauss law; We have Now, taking a cylinder of length L as a Gaussian Surface, so we…

Q: At what distance along the central axis of a uniformly charged plastic disk of radius R = 1.31 m is…

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Q: the total charge contained in a cylindrical volume defined by ρ ≤ 2 m and 0 ≤ z ≤ 3 m if ρv = 2

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Q: Calculate the electric field in N/C at point P, a distance (4.35x10^1) cm along the central axis of…

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Q: +Q R h=2R

A: Given: Radius of ring = R. Distance between center and point P = h. Charge density on ring = λ.…

Q: For which of the following charge distributions would Gauss's law not be useful for calculating the…

A: Gauss law is applicable on all the cases where it is possible to draw a symmetric gaussian surface.

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.