Home
Class 12
PHYSICS
A point charge +Q is place just outside ...

A point charge +Q is place just outside an imaginary hemispherical surface of radius R as shown in the figure. Which of the following statements is/are correct ?

A

The electric flux passing through the curved surface of the hemisphere is `- (Q)/( 2 epsi_(0)) ( 1-(1)/(sqrt(2))`

B

The component of the electric field normal to the flat surface is constant over the surface

C

Total flux through the curved and the flat surfaces is `(Q_(0))/(epsi_(0))`

D

The circumference of the flat surface is an equipotential

Text Solution

Verified by Experts

The correct Answer is:
A, D
Since the charge lies outside the hemi-sphere, net flux passing through the sphere is zero.
`phi_("curved surface")+phi_("disc")=0`
Option (C) is incorrect
`phi_("curved surface")=-phi_("disc")`
`costheta=R/(sqrt(R^(2)+r^(2))`, `phi_("disc")=intvecE.dvecA`

`=int(1/(4piepsi_(0))Q/((R^(2)+r^(2)))xx2pirdrxxcostheta)=(Q.2pi)/(4piepsi_(0))int(rdr)/(R^(2)+r^(2))xxR/((R^(2)+r^(2))^(1//2))`
`=(QR)/(2epsi_(0))int_(0)^(R)(rdr)/((R^(2)+r^(2))^(3//2))=(QR)/(2epsi_(0))[1/2((R^(2)+r^(2))^(-1//2))/(-1//2)]_(0)^(R)=(QR)/(2epsi_(0))[1/R-1/(sqrt(R^(2)+R^(2)))]=Q/(2epsi_(0))[1-1/(sqrt2)]`
`thereforephi_("curved surface")=-Q/(2epsi_(0))[1-1/(sqrt2)]` Option (A) is correct
Potential at any point on the circumference of the flat surface is `1/(4piepsi_(0))Q/(sqrt(R^(2)+R^(2)))=Q/(4piepsi_(0)(sqrt2R))`
Hence it is equipotential
Option (D) is correct
`E=1/(4piepsi_(0))Q/((R//costheta)^(2))=(theta)/(4piepsi_(0)R^(2))cos^(2)theta`
`E_("normal")=Ecostheta=Q/(4piepsi_(0)R^(2))cos^(3)theta`

Which is not constant. Option (B) is in correct
Promotional Banner

Similar Questions

Explore conceptually related problems

Locate the position of the centre of mass of a hemisphere of radius R as shown in the following figure:

q_(1),q_(2),q_(3) and q_(4) are point charges located at point as shown in the figure and s is a spherical Gaussian surface of radius R . Which of the following is true according to the Gauss's law

A charge +Q is uniformly distributed along the circular arc of radius R as shown in the figure.The magnitude of the force experienced by the point charge +q place at the centre of curvature is (k=(1)/(4piepsilon_(0)))

Figures shown electric field lines in which as electric dipole vec(p) is placed as shown .Which of the following statement is correct?

A charge q is situated at the centre of an imaginary hemispherical surface, as shown in figure. Using gauss's theorem and symmetry considerations, determine the electric flux due to this charge through the hemisphere surface.

A charge Q is placed at the centre of an inaginary hemispherical surface. Using symmetry arguments and the Gauss's law, find the flux of the electric field due to this charge through the surface of the hemisphere (figure ).

A point charge q is placed at some distance d away from the centre of a grounded conducting sphere of radius r, as shown in the figure. The charge that flows the earth to the sphere is

A point charge +Q is placed at a distance r from a short dipole of dipole moment vecp as shown in figure. The line joining the point charge Q to the centre dipole is perpendicular to dipole moment vecp , which of the following statement are true?

If a charge q is placed at the centre of imaginary sphere of radius r then the N.E.I. at a point on such a sphere is

A charge 'Q' is placed at the centre of a hemispherical surface of radius 'R'. The flux of electric field due to charge 'Q' through the surface of hemisphere is