Biot-Savart Law - UNSOLVED PRACTICE SET

Q7. State Biot-Savart Law in vector form. What does each term represent

Q8. Compare Biot-Savart Law with Coulomb's Law. List two similarities and two differences.

Q9. A current element Idl = 2 × 10⁻³ A m is oriented along the x-axis. Calculate the magnetic field at a point on the y-axis at distance r = 10 cm.

[Given: μ₀ = 4π × 10⁻⁷ T m/A]

Q10. Why is the magnetic field due to a current element always perpendicular to both the current element and the position vector?

Q11. Using Biot-Savart Law, show that the magnetic field at the center of a circular loop is perpendicular to the plane of the loop.

Q12. A student claims that Biot-Savart Law can be used to find the magnetic field due to any current distribution. Is this correct? Explain with an example where it might be difficult to apply directly.

Q13. State and explain Biot-Savart Law. Derive the expression for the magnetic field at the center of a circular loop of radius R carrying current I. Show the direction of the field using a diagram.

Q14. Using Biot-Savart Law, derive the expression for the magnetic field at a point on the axis of a circular current loop. Show that at large distances, the field behaves like that of a magnetic dipole.

Q15. A circular coil of 20 turns and radius 10 cm carries current 5 A.

(a) Calculate the magnetic field at the center of the coil.  

(b) Calculate the magnetic field at a point on the axis 10 cm from the center.  

(c) At what distance on the axis is the field half of its value at the center?  

(d) Compare the field at the center with that of a single turn carrying the same current.

[Given: μ₀ = 4π × 10⁻⁷ T m/A]

Q16. In a school physics lab, a student uses Biot-Savart Law to calculate the magnetic field due to a square loop of side 10 cm carrying current 4 A.

(a) Calculate the magnetic field at the center of the square loop.  

(b) Calculate the magnetic field at a point 5 cm above the center, perpendicular to the plane of the loop.  

(c) Compare the field at the center with that of a circular loop of the same perimeter. Which produces a stronger field?  

(d) The student replaces the square with an equilateral triangle of the same perimeter. Calculate the field at its center.  

(e) Explain why the circular loop gives the maximum field for a given perimeter.

[Given: μ₀ = 4π × 10⁻⁷ T m/A]

Q17. A Helmholtz coil consists of two identical circular coils, each with N = 100 turns and radius R = 20 cm, placed coaxially and separated by distance R. Both carry current I = 2 A in the same direction.

(a) Using Biot-Savart Law, derive the expression for the magnetic field on the axis due to one coil.  

(b) Show that the field is most uniform at the midpoint between the two coils.  

(c) Calculate the magnetic field at the midpoint.  

(d) Calculate the field at points x = 0, R/4, R/2, 3R/4, and R from the midpoint along the axis.  

(e) Explain why Helmholtz coils are used to create uniform magnetic fields in experiments.

[Given: μ₀ = 4π × 10⁻⁷ T m/A]

Q18. A long straight wire carries current I. Using Biot-Savart Law:

(a) Derive the expression for the magnetic field at perpendicular distance r from the wire.  

(b) Calculate the field at r = 5 cm from a wire carrying I = 10 A.  

(c) Two parallel wires 10 cm apart carry currents I₁ = 5 A and I₂ = 10 A in the same direction. Calculate the magnetic field at a point midway between them.  

(d) Calculate the force per unit length between the wires.  

(e) A student asks why we can't use Ampere's Circuital Law for the situation in (c) to find the field at the midpoint. Give a clear explanation.

[Given: μ₀ = 4π × 10⁻⁷ T m/A]