Home
Class 12
PHYSICS
A uniformly charged and infinitely long ...

A uniformly charged and infinitely long line having a linear charge density `'lambda'` is placed at a normal distance `y` from a point `O`. Consider a sphere of radius `R` with `O` as centre and `Rgty`. Electric flux through the surface of the sphere is

A

zero

B

`(2lambdaR)/(epsilon_0)`

C

`(2lambdasqrt(R^2-y^2))/(epsilon_0)`

D

`(lambdasqrt(R^2+y^2))/(epsilon_0)`

Text Solution

Verified by Experts

The correct Answer is:
C

Electric flux `oint_(S)ver(E).vec(d)S=(q_("in"))/(epsilon_(0))`
`q_("in")` is the charge enclosed by the gaussian surface which is the present case, is the surface of given sphere. As shown length AB of the line inside the sphere in `triangleOO'A`
`R^(2)=y^(2)+(O'A)^(2)`
or `O'A=sqrt(R^(2)-y^(2))` and `AB=sqrt(R^(2)-y^(2))`
charge on length `AB=2sqrt(R^(2)-y^(2))xxlamda`
Electric flux `oint_(S)ver(E).vec(d)S=(2lamdasqrt(R^(2)-y^(2)))/(epsilon_(0))`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS VOLUME 3

    CENGAGE PHYSICS ENGLISH|Exercise Assertion and Reason Type|8 Videos

  • MISCELLANEOUS VOLUME 3

    CENGAGE PHYSICS ENGLISH|Exercise Comprehension Type|94 Videos

  • MAGNETIC FIELD AND MAGNETIC FORCES

    CENGAGE PHYSICS ENGLISH|Exercise Multiple Correct Answer type|2 Videos

  • MISCELLANEOUS VOLUME 5

    CENGAGE PHYSICS ENGLISH|Exercise Integer|12 Videos

Similar Questions

Explore conceptually related problems

An infinitely long line charge having a uniform charge per unit length lambda lies at a distance d from a point O as shown in figure. Determine the total electric flux through through the surface of a sphere of radius R centered at O resulting from this line charge. Consider both cases where Rltd and Rgtd .

An infinitely long line charge having a uniform charge per unit length lambda lies at a distance d from a point O as shown in figure. Determine the total electric flux through through the surface of a sphere of radius R centered at O resulting from this line charge. Consider both cases where Rltd and Rgtd .

A point charge q is placed at a distance d from the centre of a circular disc of radius R. Find electric flux flowing through the disc due to that charge

A charge q_0 is distributed uniformly on a ring of radius R. A sphere of equal radius R constructed with its centre on the circumference of the ring. Find the electric flux through the surface of the sphere.

Electric field at centre O of semicircule of radius 'a' having linear charge density lambda given is given by

Consider an infinite line charge having uniform linear charge density and passing through the axis of a cylinder is removed.

A point charge q , is placed at a distance r from the centre of an aluminium sphere, of radius R ( r gt R ) . Selectr the correct alternatives.

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 hallow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre:

The electric field at distance .r. from infinte line of charge ("having linear charge density" lambda) is