Advertisements
Advertisements
Question
A hollow cylindrical box of length 0.5 m and area of cross-section 25 cm2 is placed in a three dimensional coordinate system as shown in the figure. The electric field in the region is given by `vecE = 20 xhati` where E is NC−1 and x is in metres. Find
(i) Net flux through the cylinder.
(ii) Charge enclosed by the cylinder.
Advertisements
Solution
(i) Given,
As the electric field is only along the x-axis, so, flux will pass only through the cross-section of cylinder.
Magnitude of electric field at A,
`E_A = 20 xx 0.5 = 10 N C^-1`
Magnitude of lelectic field at cross - section B
EB = 20 × 1= 20 NC-1
The corresponding eletric fluxes are
`phi_A = vecE.Δvecs = 10 xx 20 xx 10^-4 xx cos 180° = - 0.02 N m^2 C^-1`
`phi_B = vecE.Δvecs = 20 xx 20 xx 10^-4 xx cos0° = 0.04 N m^2 C^-1`
So, the net flux through the cylinder,
`phi = phi _A + phi_B = - 0.02 + 0.04 = 0.02 N m^2 C^-1 xx 10^12C`
(ii) Using Gauss’s law:
`oint vecE. vecds = q/in_0 => 0.02 = q/(8.85 xx 10^-12) => q =8.85 xx 0.02 xx 10^-12 = 0.177 xx 10^12 C`
APPEARS IN
RELATED QUESTIONS
An infinite line charge produces a field of 9 × 104 N/C at a distance of 2 cm. Calculate the linear charge density.
Show that if we connect the smaller and the outer sphere by a wire, the charge q on the former will always flow to the latter, independent of how large the charge Q is.
Consider a system of n charges q1, q2, ... qn with position vectors `vecr_1,vecr_2,vecr_3,...... vecr_n`relative to some origin 'O'. Deduce the expression for the net electric field`vec E` at a point P with position vector `vecr_p,`due to this system of charges.
A hollow cylindrical box of length 1 m and area of cross-section 25 cm2 is placed in a three dimensional coordinate system as shown in the figure. The electric field in the region is given by `vecE = 50xhati` where E is NC−1 and x is in metres. Find
(i) Net flux through the cylinder.
(ii) Charge enclosed by the cylinder.
Can a gravitational field be added vectorially to an electric field to get a total field?
Which of the following quantities does not depend on the choice of zero potential or zero potential energy?
An electric field \[\vec{E} = ( \vec{i} 20 + \vec{j} 30) {NC}^{- 1}\] exists in space. If the potential at the origin is taken to be zero, find the potential at (2 m, 2 m).
The electric potential existing in space is \[\hspace{0.167em} V(x, y, z) = A(xy + yz + zx) .\] (a) Write the dimensional formula of A. (b) Find the expression for the electric field. (c) If A is 10 SI units, find the magnitude of the electric field at (1 m, 1 m, 1 m).
Consider a region inside which, there are various types of charges but the total charge is zero. At points outside the region ______.
