The figure above shows a closed Gaussian surface in the shape of a cube of edge length d. It lies in a region where the electric field is given by E = (ax + a)î+ bj + ck. What is the net charge contained %3D by the cube?
Q: Consider a cube with edge length Limmersed in a uniform electric field E along the x-direction as…
A: Solution: The expression of electric flux is given by: ϕE=∫SE→.n^dS; where, E→ is the electric…
Q: An electric field given by É = 6.4 i - 5.2(y? + 7.3) ĵ pierces the Gaussian cube of edge length…
A: Answer is -0.256 Nm²/C .
Q: The figure shows a spherical Gaussian surface with radius R and a long straight charged wire with…
A: For calculating the total electric flux, Gauss's law can be used. And the gauss's law states that…
Q: Consider a cube with edge length L immersed in a uniform electric field E along the x-direction as…
A: Let us assume a cube with an edge length L that is immersed in a uniform electric field E along its…
Q: Three infinite nonconducting sheets, with uniform positive surface charge densities 0, 20, and 30,…
A: We have to apply Gauss law here, for parallel charged sheets E= (charge density) / ( Permittivity of…
Q: Consider a cube with edge length L immersed in a uniform electric field E along the x-direction as…
A: The net flux is the sum of the fluxes through all faces of the cube. First, note that the flux…
Q: An electric field given by = 4.8 - 2.7(y2 + 7.5) pierces the Gaussian cube of edge length 0.460 m…
A: The figure with the direction vectors is shown below:
Q: An electric field given by = 5.5i - 2.3(y2 + 5.8)j pierces the Gaussian cube of edge length 0.210 m…
A: Electric flux is defined as a effective number of electric field lines passing through a given cross…
Q: Consider a cube with edge length Limmersed in a uniform electric field E along the x-direction as…
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Q: A cone is as shown in the figure with its face is in the xy-plane. A uniform electric field of…
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Q: Inside the region in the shape ( Rectangular box) there is no electric charge. The uniform electric…
A: The given electric field is, E→=4i^-6j^ The -6j part of the vector is not passing the box so it will…
Q: Two infinite, nonconducting sheets of charge are parallel to each other . The sheet on the left has…
A: Two charged plates of surface charge densities −σ & σ are given.
Q: If the electric flux density is given by D = x²a, + y²z a,y determine the m volume charge density at…
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Q: A thin, circular plate of radius B, uniform surface charge density a, and total charge Q, is…
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Q: The figure shows a Gaussian surface in the shape of a cube with edge length 1.60 m. What are (a) the…
A: Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any…
Q: The figure here shows a Gaussian cube of face area A immersed in a uniform electric field that has…
A: NOTE-Since you have posted a question with multiple sub-parts, we will solve first three sub parts…
Q: An insulating sphere with radius a has uniform charge density p but is centred at b. a) Show the…
A: (a) Let b denotes the position vector of the center of the charged sphere, rp denotes the position…
Q: An infinite, uniformly charged sheet with surface charge density o cuts through a spherical Gaussian…
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Q: An electric field given by É =4.5 i - 4.6(y² + 1.3)j pierces the Gaussian cube of edge length 0.130…
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Q: Calculate the absolute value of the electric flux for the following situations (In all case provide…
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Q: An electric field given by É =6.4î - 5.2(y2 + 7.3) ĵ pierces the Gaussian cube of edge length 0.200…
A:
Q: Find the net electric flux through the spherical closed surface shown in the figure below. The two…
A: q1 = 1.84 nC q2 = 1.04 nC q3 = -3.06 nC
Q: The figure below represents the top view of a cubic gaussian surface in a uniform electric field E…
A: According to guideline we need to solve only first three sub part . The figure belov represents the…
Q: Consider a cube with edge length L immersed in a uniform electric field E along the x-direction as…
A: Consider a cube with edge length L immersed in a uniform electric field E along the x-direction. The…
Q: y ro/3 Po ro A A sphere of Radius r, carries a constant volume charge density Po as seen in the…
A: ELECTRIC FIELD INSIDE THE SOLID SPHERE = q in = ρ0 (4/3 πr03/27) ρ0 = volume charge density And we…
Q: Two infinite, nonconducting sheets of charge are parallel to each other, as shown above. The sheet…
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Q: A square 10 cm long is in a region where there exists a uniform 2.0 kN/C electric field normal to…
A: Given data: Side of square (s) = 10 cm = 0.1 m Electric field (E) = 2.0 kN/C = 2000 N/C Angle…
Q: An electric field given by E-8.6i - 7.8(y2 + 8.1) pierces the Gaussian cube of edge length 0.950 m…
A: Electric flux can be defined as the total number of electric field lines passing through a given…
Q: The figure shows a sphere carrying a uniformly distributed volume charge Q. Three Gaussian surfaces…
A: The gaussian surfaces, which are concentric are shown in the figure.
Q: An infinite sheet lie on the xz plane and z axis points outward from the page (not shown). A solid…
A:
Q: Consider a cube with edge length L immersed in a uniform electric field E along the x-direction as…
A: Given data: Edge length = l Electric field =E
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: A point charge Q is located on the axis of a disk of radius R at a distance h from the plane of the…
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Q: Consider the closed Gaussian surface shown below. Calculate the total net electric flux through the…
A: The enclosed charge inside the Gaussian surface is:
Q: Consider a cube with edge length L immersed in a uniform electric field E along the x-direction as…
A:
Q: A uniform electric field measured over a square surface with side length d = 15.5 cm makes an angle…
A: Given: d = 15.5 cm angle θ = 67.0° Electric flux = 5.40 N m2/C
Q: An infinite line charge has constant charge-per-unit-length λ. Surrounding the line charge is a…
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Q: The figure bēlöw depicts the (a) State which of the charges 1,2 and 3 are positive or negative. (b)…
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Q: The figure shows a closed Gaussian surface in the shape of a cube of edge length 1.5 m, with one…
A: Given information:Length of the gaussian cube (l) = 1.5 mThe co-ordinates of one edge of the…
Q: E, = bx? Let the distribution of electric field strength in a certain area of space be y E, = E. = 0…
A: Given,
Q: Consider a cube with edge length L immersed in a uniform electric field E along the x-direction as…
A: Given data: The edge of the cube is, L The uniform electric field is in the positive direction of…
Q: what is the magnitude.of the electric flux of a constant E of 4 n/c in the z direction through a…
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Q: A nonuniform electric field given by 3xî + 4ĵ pierces the Gaussian cube shown in Figure (E is in…
A: Given data: The electric field, E→=3xi⏜+4j⏜. Since the front face of the Gaussian cube is between…
Q: Rank the electric fluxes through each gaussian surface shown in the figure from largest to smallest.…
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Q: A charge distribution that is spherically symmetric but not uniform radially produces an electric…
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Q: Figure shows a point charge Q= 2 nC placed at origin and a very long line carrying free charge with…
A: Given:point charge of Q = +2 nC at (0,0,0)mline charge oriented perpendicular to x-y planeρ = +0.5…
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- Consider an infinitesimal segment located at an angular position θ on the semicircle, measured from the lower right corner of the semicircle at x=a, y=0. (Thus θ=π2 at x=0, y=a and θ=π at x=−a, y=0.) What are the x- and y- components of the electric field at point P (dEx and dEy) produced by just this segment? Express your answers separated by a comma in terms of some, all, or none of the variables Q, a, θ, dθ, and the constants k and π.Determine the total charge distribution on r = b, and on r = a., explain Check if the electrical field for this configuration match the findings that for all points r inside the circle r<a is E= q/4piΕor2 and for all points r outside the shell r>a is E=0A uniform electric field measured over a square surface with side length d = 15.5 cm makes an angle θ = 67.0° with a line normal to that surface, as shown in the figure below. There is a square horizontal surface with length and width d. The surface has a normal vertical axis at the center with a vector labeled vector E traveling from the center of the plane up and to the right. Vector E and the normal vertical axis form an angle labeled θ. If the net flux through the square is 5.40 N · m2/C, what is the magnitude Eof the electric field (in N/C)? N/C
- A solid insulating plastic sphere of radius a carries atotal net positive charge 3Q uniformly distributed throughout its interior.The insulating sphere is coated with a metallic layer of inner radius a andouter radius 2a. The conducting metallic layer carries a net charge of -2Q. Apply Gauss’s law to find the magnitude of the electric field in the region r < a. Inthe figure, draw the Gaussian surface you are using, and indicate on that surface the direction of anyvectors which appear in the mathematical expression of Gauss’s law. Express your answer in terms ofa, Q, r, and ε0. (If you get an expression involving ρ, substitute it from above to re-express youranswer in terms of the stated variables.)Consider the three-dimensional conductor in the figure, that has a hole in the center. The conductor has an excess charge 7.2 μC on it. What is the electric flux (in N⋅m2/C) through the Gaussian surface S1 shown in the figure? Now put a point of charge 27.4 μC inside the cavity of the conductor. What is the flux (in N⋅m2/C) through the Gaussian surface S1? Now consider the Gaussian surface S2. With the charge still inside the cavity, what is the flux (in Nm2/C) through this surface?Examine the summary on page 780. Why are conductors and charged sources with linear symmetry, spherical symmetry, and planar symmetry categorized as special cases rather than major concepts or underlying principles?
- Consider two concentric insulating cylinders of infinite length. The inner cylinder is solid with radius R, while the outer cylinder is a hollow shell with inner radius a and outer radius b. Both cylinders have the same volume charge density of +ρ. Using Gauss’s Law, find the electric field as a function of r (where r= 0 at the central axis) in the interval a≤r < b. Note: Your final equation should be in terms of given parameters of ρ,a,b,R, and r.Figure 2 shows a nonconducting rod with a uniformly distributed charge Q. The rod forms a half-circle with radius R and produces an electric field of magnitude Earc at its center of curvature P. If the arc is collapsed to a point at distance R from P, by what factor is the magnitude of the electric field at P multiplied?A thin, circular plate of radius B, uniform surface charge density, and total charge Q, is centered on the origin and lies in the x-y plane. What is the electric flux ΦE through a sphere of radius r, also centered on the origin, as a function of r? Consider both (a.) r > B and (b.) r < B:
- If a closed cylindrical surface of height 0.3 m and diameter 0.2 m were placed as shown, completely enclosing q1 and q3, what would be the net flux through the surface due to all three charges?A large non-conducting slab of area A and thickness d has a charge density rho=Cx^4. The origin is through the center of the slab. That is to say, it bisects the slab into two equal volumes of d/2 thickness and with an area of A, with -d/2 to the left of x=0, and d/2 to the right of x=0. Express all answers in terms of C, x, and any known constants. Gaussian surface 1 (cylinder) is located such that its volume encompasses the charge contained within the slab. Apply Gauss's Law to cylinder 1 to determine the electric field to the left and to the right of the slab. Make sure you incude the domains over which the field is valid.Consider a uniform electric field of E = (a, b, 0) and a disk of radius R What is the flux through the disk if it sits in the yz-plane? What is the flux through the disk if it sits in the xy-plane? What is the maximum flux through the disk as it rotated through all possible orientations?