Electric Flux - UNSOLVED PRACTICE SET

Q7. Define electric flux. Write its expression for a uniform electric field passing through a flat surface at an angle θ to the field.

Q8. A rectangular surface of area A is placed in a uniform electric field E. How does the electric flux change if the surface is rotated from θ = 0° to θ = 90°?

Q9. What is a free body diagram? Why is it useful in solving physics problems involving forces?

Q10. A small charged sphere is suspended by a thread in a uniform horizontal electric field. Draw the free body diagram showing all forces acting on the sphere.

Q11. Explain why the electric flux through a closed surface containing no charge is zero.

Q12. A charged oil drop of mass m and charge q is held stationary between two parallel plates with a uniform electric field E. Write the condition for equilibrium using a free body diagram approach.

Q13. Explain the concept of electric flux with a clear diagram. Show how the flux depends on the orientation of the surface relative to the electric field. What is the flux when the surface is parallel to the field?

Q14. Describe the steps to draw a free body diagram for a charged particle moving in a uniform electric field. Illustrate with an example of a positively charged particle projected horizontally into a downward uniform electric field.

Q15. A square loop of side 10 cm is placed in a uniform electric field E = 200 N/C. The plane of the loop makes an angle of 60° with the direction of the field.

(a) Calculate the electric flux through the loop.

(b) If the loop is rotated so that its plane becomes perpendicular to the field, what is the new flux?

(c) What is the flux when the plane of the loop is parallel to the field?

Q16. A small sphere of mass 2 g and charge +5 μC is suspended by a light insulating thread of length 50 cm in a uniform horizontal electric field E = 2 × 10⁴ N/C.

(a) Draw a clear free body diagram showing all forces acting on the sphere.

(b) Calculate the tension in the thread.

(c) Find the angle that the thread makes with the vertical when the sphere is in equilibrium.

[Given: g = 9.8 m/s²]

Q17. In Millikan's oil drop experiment, a tiny oil drop of radius 1.2 × 10⁻⁶ m and density 900 kg/m³ is held stationary between two horizontal parallel plates separated by 2 cm. The potential difference between the plates is 1200 V.

(a) Draw the free body diagram for the oil drop.

(b) Calculate the charge on the oil drop.

(c) How many excess electrons does the drop carry?

(d) What would happen if the potential difference is increased slightly?

[Given: g = 9.8 m/s², ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²]

Q18. A cube of side 2 m is placed in a region with a uniform electric field E = (4î + 3ĵ) N/C.

(a) Calculate the electric flux through each face of the cube.

(b) What is the total flux through the entire closed surface of the cube?

(c) Using Gauss's Law, what can you conclude about the net charge enclosed within the cube?

(d) A charge of +2 μC is now placed at the center of the cube. Calculate the new total flux through the cube.

[Given: ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²]