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If the electric field is given by 26i – k. Calculate the electric flux through a surface of area 20 units lying in xy plane.
► Electric field (E) = 26i  k
► A = 20k
Electric flux = electric field.area
= E.A
= (26i  k)*(20k)
= (26*0 1)*20
= 20 units
A point charge of 2.0 μC is at the center of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
Net electric flux (Φ_{Net}) through the cubic surface is given by,
Where, ∈_{0} = Permittivity of free space
= 8.854 × 10^{−12} N^{−1}C^{2} m^{−2}
q = Net charge contained inside the cube = 2.0 μC = 2 × 10^{−6} C
∴
= 2.2 × 10^{5} N m^{2} C^{−1}
The net electric flux through the surface is 2.2 ×10^{5} N m^{2}C^{−1}.
Electric flux through an area dA for an electric field E is given by:
For constant electric field
A point charge causes an electric flux of −1.0×10^{3} Nm^{2}/C to pass through a spherical Gaussian surface of 10.0 cm radius centered on the charge.
(a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?
(b) What is the value of the point charge?
Electric flux is given by since amount of charge not depends on size and shape so by making radius < double the amount of charge remain same so electric flux remain same.
By definition of Solid Angle,
Where, Ω is represented in Steradians.
Electric flux is a scalar quantity. Electric Flux is dot/scalar product of magnetic field vector and area vector. And the result of a dot/scalar quantity is always a scalar quantity. So electric flux is also a scalar quantity
If the electric field is given by 6i+3j+4k calculate the electric flux through a surface of area 20 units lying in yz plane.
► Area = 20i since it is in the YZ plane
► E = 6i + 3j + 4k
► E.S = Flux
= 20*6 = 120 units
A uniform line charge with linear density λ lies along the yaxis. What flux crosses a spherical surface centred at the origin with r = R?
Line charge density = λ
Radius, r = R
Now, λdl=dθ
For total charge enclosed by radius R, _{0}∫^{R} Q = _{0}∫^{R} λdl
Q_{inc} = λR
Now, ϕ = Q_{inc}/ε_{o} {from Gauss law}
= λR/ε_{0}
Flux = E. A
⇒ F = Eq
⇒ E= F/q= N/C
⇒ Flux= N/C × m²
= Nm^{2}C^{1}
Electric flux density is the charge per unit area. Hence it is a function of charge and not any of the other values.
Which of the following correctly states Gauss law?
The electric flux passing through any closed surface is equal to the total charge enclosed by that surface. In other words, electric flux per unit volume leaving a point (vanishing small volume), is equal to the volume charge density
By definition,
For maximum, E.dA must be maximum. This is possible when E  dA.
A point charge is single dimensional. The three dimensional imaginary enclosed surface of a point charge will be sphere.
At what point is the electric field intensity due to a uniformly charged spherical shell is maximum?
By Gauss Law,
Electric Field due to spherical shell shows the following behavior:
A charge q is placed at the centre of the open end of cylindrical vessel whose height is equal to its radius. The electric flux of electric field of charge q through the surface of the vessel is
We can assume a similar vessel, such that the charge lies at the interfaces of both the vessels. Now, by Gauss law, all the electric flux must pass through these two vessels. As they are kept symmetrically with respect to the charge equal amount of flux would pass through them
From both vessels,
For each vessel,
The charge enclosed by a spherical Gaussian surface is 8.85 X 10^{8} C. What will be the electric flux through the Surface?
We know that the flux linked with a Gaussian surface is given as:
Φ = E.ds = q/ε_{0}
Here,
q = 8.85 x 10^{8} C
ε_{0} = 8.85 x 10^{12} F/m
So,
Φ = 8.85x10^{8}/ 8.85x10^{12}
Thus, flux will be
Φ = 10^{4} Nm^{2}/C
If the electric field is given by calculate the electric flux through as surface of area 10 units lying in yz plane.
Hence,
The flux associated with a spherical surface is 10^{4} N m^{2}C^{1}. What will be the flux, if the radius of the spherical shell is doubled?
If the radius of the spherical shell is double then also flux associated with spherical surface remain unchanged because the charge enclosed in system always remains unchanged.
A line charge can be visualized as a rod of electric charges. The three dimensional imaginary enclosed surface of a rod can be a cylinder.
The electric field intensity due to a sphere (solid or hollow) at an external point varies as:
We calculate this using spherical symmtery in Gauss Law
For spherical Shell,
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