A long cylindrical volume contains a uniformly distributed charge of density . The radius of cylindrical volume is . A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :
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A solid conducting sphere of radius a has a net positive charge . A conducting spherical shell of inner radius and outer radius is concentric with the solid sphere and has a net charge .The surface charge density on the inner and outer surfaces of the spherical shell will be
None of the above
Surface charge density
If electric field in a region is radially outward with magnitude , the charge contained in a sphere of radius centred at the origin is
Let be the charge density distribution for a solid sphere of radius and total charge . For a point ' ' inside the sphere at distance from the centre of the sphere, the magnitude of electric field is :
0
The Gaussian surface
can pass through a continuous charge distribution.
cannot pass through a continuous charge distribution.
can pass through any system of discrete charges.
can pass through a continuous charge distribution as well as any system of discrete charges.
Gaussian surface cannot pass through any discrete charge because electric field due to a system of discrete charges is not well defined at the location of the charges. But the Gaussian surface can pass through a continuous charge distribution.
Which statement is true for Gauss law-
All the charges whether inside or outside the gaussian surface contribute to the electric flux.
Electric flux depends upon the geometry of the gaussian surface.
Gauss theorem can be applied to non-uniform electric field.
The electric field over the gaussian surface remains continuous and uniform at every point.
All other statements except (iv) are in correct.
The electric field over the Gaussian surface remains continuous and uniform at every point.
The total electric flux emanating from a closed surface enclosing an -particle is (e-electronic charge)
According to Gauss's law total electric flux through a closed surface is times the total charge inside that surface.
Electric flux,
Charge on -particle
For a given surface the Gauss's law is stated as . From this we can conclude that
is necessarily zero on the surface
is perpendicular to the surface at every point
the total flux through the surface is zero
the flux is only going out of the surface
, represents charge inside close surface is zero. Electric field as any point on the surface may be zero.
The electric field inside a spherical shell of uniform surface charge density is
zero
constant different from zero
proportional to the distance from the curve
Electric charge resides only on the surface of a spherical shell. According to Gauss's theorem the total electric flux over a closed surface is equal to the times the total charge enclosed by the closed surface.
A charge is placed at the centre of the open end of a cylindrical vessel. The flux of the electric field through the surface of the vessel is
The flux is zero according to Gauss' Law because it is a open surface which enclosed a charge .
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