Magnetic Flux - UNSOLVED PRACTICE SET

Q7. Define magnetic flux. Write its expression when the magnetic field makes an angle θ with the normal to the surface.

Q8. A square loop of side 15 cm is placed in a uniform magnetic field of 0.4 T. Calculate the magnetic flux when (a) the plane is perpendicular to the field, and (b) the plane makes 60° with the field.

Q9. Why is magnetic flux a scalar quantity even though magnetic field is a vector? Explain.

Q10. A coil of 100 turns and area 20 cm² is placed in a magnetic field of 0.3 T perpendicular to the coil. Calculate the flux linkage.

Q11. What happens to the magnetic flux through a loop if the magnetic field is doubled and the loop area is halved? Explain.

Q12. A circular loop of radius r is placed in a uniform magnetic field B. The loop is then stretched to an ellipse with the same perimeter. Does the flux change? Explain.

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

Q14. A rectangular loop of dimensions 20 cm × 30 cm is placed in a uniform magnetic field B = 0.6 T. The loop can rotate about an axis in its plane.

(a) Calculate the maximum flux through the loop.

(b) Calculate the flux when the normal to the loop makes 45° with the field.

(c) Calculate the flux when the plane of the loop is parallel to the field.

(d) If the loop rotates from position (a) to position (c) in 0.2 s, calculate the average induced EMF (assuming 50 turns).

Q15. A cube of side 10 cm is placed in a uniform magnetic field B = 0.5 T directed along the positive x-axis.

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

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

(c) What does this result tell you about magnetic field lines?

(d) Compare this with Gauss's law for electric fields and explain the difference.

Q16. In a school physics lab, a student uses a circular coil of radius 8 cm with 150 turns to study magnetic flux. The coil is placed in a uniform magnetic field that varies with time as B(t) = 0.2 + 0.1t (where B is in Tesla and t is in seconds).

(a) Calculate the magnetic flux through the coil at t = 0 and t = 5 s.

(b) Calculate the rate of change of flux at any time t.

(c) Calculate the induced EMF in the coil.

(d) If the coil resistance is 5 Ω, calculate the induced current at t = 3 s.

(e) The student places an identical coil perpendicular to the first one. Calculate the total flux linkage through both coils at t = 2 s.

Q17. A rectangular conducting loop with sides a = 20 cm and b = 30 cm is moved with constant velocity v = 5 m/s into a region of uniform magnetic field B = 0.4 T directed perpendicular to the plane of the loop. The loop has resistance R = 2 Ω.

(a) Calculate the magnetic flux through the loop as a function of the distance x that the loop has entered the field region.

(b) Calculate the rate of change of flux.

(c) Calculate the induced EMF and current while the loop is entering.

(d) Calculate the magnetic force opposing the motion.

(e) What power must be supplied to maintain the constant velocity? Verify that this equals the power dissipated as heat in the loop.

Q18. A solenoid of length 50 cm, radius 3 cm, and 1000 turns carries current I = 2 A. A small circular loop of radius 1 cm and 50 turns is placed coaxially at the center of the solenoid.

(a) Calculate the magnetic field inside the solenoid.

(b) Calculate the magnetic flux through the small loop.

(c) If the solenoid current is reduced to zero in 0.1 s, calculate the induced EMF in the small loop.

(d) Calculate the mutual inductance between the solenoid and the small loop.

(e) A student moves the small loop to the end of the solenoid. How does the flux change? Explain.

[Given: μ₀ = 4π × 10⁻⁷ T m/A]