Rank the situations of Question 9 according to the magnitude of the electric field
(a) halfway through the shell and
(b) at a point from the center of the shell, greatest first.
A charge ball lies within a hollow metallic sphere of radius R .
The net charges of the ball and the shell for three situations are given.
Using the electric field concept for a hollow metallic sphere, you can get the required rank of the situations. Due to its properties, the charges of a hollow sphere remain at the surface of the sphere. Thus, the charge inside the shell is zero and so its electric field is also zero. Similarly, the electric field at any point at the surface or above surface is given by the surface charges and the distance of the point from the center of the shell.
The electric field at any point outside the hollow metallic sphere,
Where, Q is the outer charge of the shell, K is the Coulomb’s constant, and r is the distance.
The electric field at any point inside a hollow metallic sphere is
Hence, the rank of the situations according to the electric field at halfway is .
Consider a Gaussian surface at a distance from the center. Here, the distance of the point is given by
Thus, the point is outside the shell. So, the magnitude of electric fields for the three situations including its outer charge value is given by,
Here, R is the radius of the spherical shell, is the charge on the ball, and is the charge on the shell.
The magnitude of the electric field for situation 1 when the charge on the ball is and on the shell is zero.
The magnitude of the electric field for situation 2 when the charge on the ball is and on the shell is .
The magnitude of the electric field for situation 3 when the charge on the ball is and on the shell is .
Hence, the rank of the situations according to field value is
The box-like Gaussian surface shown in Fig. 23-38 encloses a net charge of and lies in an electric field given by role="math" localid="1657339232606" with x and z in meters and b a constant. The bottom face is in the plane; the top face is in the horizontal plane passing through . For , , , and , what is b?
A charge of uniform linear density 2.0nC/m is distributed along a long, thin, non-conducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius=5.0 cm , outer radius=10 cm ). The net charge on the shell is zero. (a) What is the magnitude of the electric field from the axis of the shell? What is the surface charge density on the (b) inner and (c) outer surface of the shell?
Water in an irrigation ditch of width w = 3.22m and depth d = 1.04m flows with a speed of 0.207 m/s. The mass flux of the flowing water through an imaginary surface is the product of the water’s density (1000 kg/m3) and its volume flux through that surface. Find the mass flux through the following imaginary surfaces:
(a) a surface of area wd, entirely in the water, perpendicular to the flow;
(b) a surface with area 3wd / 2, of which is in the water, perpendicular to the flow;
(c) a surface of area wd / 2, , entirely in the water, perpendicular to the flow;
(d) a surface of area wd , half in the water and half out, perpendicular to the flow;
(e) a surface of area wd , entirely in the water, with its normal from the direction of flow.
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