Physics Class 12 NCERT Solutions: Chapter 1 Electric Charges and Fields Part 5

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Formula of electric flux

Formula of Electric Flux

Q: 16. What is the net flux of the uniform electric field of Exercise (Reference: Chapter 1 Electric Charges And Fields Part 4) through a cube of side oriented so that its faces are parallel to the coordinate planes?

Answer:

All the faces of a cube are parallel to the coordinate axes. Therefore, the number of field lines entering the cube is equal to the number of field lines piercing out of the cube. As a result, net flux through the cube is zero.

Q: 17. Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is. (A) What is the net charge inside the box? (B) If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or why not?

Answer:

(A) Net outward flux through the surface of box, for a body containing net charge flux is given by the relation,

Therefore, the net charge inside the box is.

(B) No

Net flux piercing out through a body depends on the net charge contained in the body. If net flux is zero, then it can be inferred that net charge inside the body is zero. The body may have equal amount of positive and negative charges.

Q: 18. A point charge is a distance 5cm directly above the centre of a square of side, as shown in fig. 1.34. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge.)

Q 18 The Square as One Face of a cube with edge 10cm

Q 18 the Square as One Face of a Cube with Edge 10cm

Answer:

The square can be considered as one face of a cube of edge 10 cm with a centre where charge q is placed. According to Gauss’s theorem for a cube, total electric flux is through all its six faces.

Hence, electric flux through one face of the cube i.e., through the square,

Where,

Permittivity of free space

Therefore, electric flux through the square is .

Q: 19. A point charge of is at the centre of a cubic Gaussian surface on edge.

What is the net electric flux through the surface?

Answer:

Net electric flux through the cubic surface is given by,

Where,

Permittivity of free space

Net charge contained inside the cube

The net electric flux through the surface is .

Q: 20. A point charge causes an electric flux of to pass through a spherical Gaussian surface of radius centered on the charge. (A) If the radius of the Gaussian surface were doubled, how mush flux would pass through the surface? (B) What is the value of the point charge?

Answer:

(A) Electric flux,

Radius of the Gaussian surface,

Electric flux piercing out through a surface depends on the net charge enclosed inside a body. It does not depend on the size of the body. If the radius of the Gaussian surface is doubled, then the flux passing through the surface remains the same .

(B) Electric flux is given by the relation,

Where,

Net charge enclosed by the spherical surface

Permittivity of free space

Therefore, the value of the point charge is.