Magnetic Field due to Straight Wire and Circular Loop - UNSOLVED PRACTICE SET
Chapter: Moving Charges and Magnetism | Topic: Magnetic Field due to Straight Wire and Circular Loop
MAGNETIC FIELD DUE TO STRAIGHT WIRE AND CIRCULAR LOOP - UNSOLVED PRACTICE SET
Topic: Magnetic Field due to Straight Wire and Circular Loop
Multiple Choice Questions
Q1. The magnetic field at perpendicular distance r from a long straight current-carrying wire is:
- μ₀I/2πr
- μ₀I/4πr
- μ₀I/2r
- μ₀I/r²
Q2. The magnetic field at the center of a circular loop of N turns, radius R, carrying current I is:
- μ₀NI/2R
- μ₀NI/4R
- μ₀NI/2πR
- μ₀I/2NR
Q3. The magnetic field lines around a long straight current-carrying wire are:
- Straight lines parallel to the wire
- Concentric circles in a plane perpendicular to the wire
- Radial lines outward from the wire
- Ellipses around the wire
Q4. The magnetic field at a point on the axis of a circular loop at distance x from the center is:
- μ₀NIR²/2(R² + x²)^(3/2)
- μ₀NIR/2(R² + x²)
- μ₀NI/2(R² + x²)^(1/2)
- μ₀NIR²/(R² + x²)
Q5. For a long straight wire, the magnetic field:
- Increases with distance from the wire
- Decreases linearly with distance
- Decreases inversely with distance
- Is independent of distance
Q6. The direction of magnetic field at the center of a circular loop carrying current clockwise is:
- Upward (out of the plane)
- Downward (into the plane)
- Along the tangent
- Radially outward
Short Answer Questions
Q7. Derive the expression for the magnetic field at perpendicular distance r from an infinitely long straight current-carrying wire using Ampere's Circuital Law.e...
Q8. A long straight wire carries current 10 A. Calculate the magnetic field at distance (a) 5 cm, and (b) 10 cm from the wire.
[Given: μ₀ = 4π × 10⁻⁷ T m/A]
Q9. Draw the magnetic field lines for (a) a long straight wire carrying current upward, and (b) a circular loop carrying current clockwise (viewed from above).
Q10. A circular coil of 50 turns and radius 5 cm carries current 2 A. Calculate the magnetic field at its center.
Q11. Two parallel wires carry currents in the same direction. Describe the magnetic field at a point midway between them.
Q12. Why is the magnetic field at the center of a circular loop stronger than at points away from the center along the axis?
Long Answer Questions
Q13. Derive the expression for the magnetic field at a point on the axis of a circular current loop. Show that the field is maximum at the center and decreases as we move away along the axis. Draw a graph of B versus x.
Q14. Two coaxial circular loops of radii R₁ and R₂ carry currents I₁ and I₂ in the same direction. They are separated by distance d. Derive the expression for the magnetic field at a point on their common axis midway between them. Under what condition is the field uniform in the region between the loops?
Q15. A long straight wire carries current I = 15 A. A circular loop of radius r = 5 cm is placed with its center at distance d = 10 cm from the wire. The loop carries current I₂ = 5 A.
(a) Calculate the magnetic field at the center of the loop due to the straight wire.
(b) Calculate the magnetic field at the center due to the loop itself.
(c) What is the net field at the center if both currents flow in directions that produce fields in the same direction?
(d) If the loop is free to move, describe its motion.
[Given: μ₀ = 4π × 10⁻⁷ T m/A]
Numerical / Application-Based Problems
Q16. In a school lab, students study the magnetic field around a long straight wire using a compass needle. The wire carries I = 8 A and is aligned north-south.
(a) Calculate the magnetic field at distance 2 cm, 5 cm, and 10 cm from the wire.
(b) At 2 cm from the wire, the compass needle deflects by 60° from magnetic north. Calculate the horizontal component of Earth's magnetic field at that location.
(c) If the current is reversed, what is the new deflection of the compass needle?
(d) The students place a second parallel wire 4 cm away carrying I = 6 A in the opposite direction. Calculate the net field at the midpoint.
(e) Explain why the compass method is a simple but effective way to demonstrate Oersted's discovery.
[Given: μ₀ = 4π × 10⁻⁷ T m/A]
Q17. A circular coil of N = 100 turns and radius R = 10 cm is placed in the y-z plane with its center at the origin. It carries current I = 3 A counterclockwise when viewed from the positive x-axis.
(a) Calculate the magnetic field at the center of the coil.
(b) Calculate the magnetic field at point P on the x-axis at x = 10 cm.
(c) A long straight wire parallel to the y-axis passes through point (20 cm, 0, 0) carrying current I₂ = 5 A in the +y direction. Calculate the total field at the origin due to both the coil and the wire.
(d) Calculate the force on a charge q = +2 μC moving with velocity v = 4 × 10⁵ m/s along the x-axis at the origin.
(e) A student places a small compass at the origin. In which direction will it point? Explain.
[Given: μ₀ = 4π × 10⁻⁷ T m/A]
Q18. Two identical circular coils, each with N = 50 turns and radius R = 15 cm, are placed coaxially 15 cm apart (Helmholtz arrangement). Both carry current I = 4 A in the same direction.
(a) Calculate the magnetic field at the center of each coil.
(b) Calculate the magnetic field at the midpoint between the coils.
(c) Calculate the field at points x = 0, 3.75 cm, 7.5 cm from the midpoint along the axis.
(d) Show that the field is most uniform near the midpoint by calculating dB/dx at the midpoint.
(e) Explain why this arrangement is used in experiments requiring uniform magnetic fields, such as calibrating magnetometers.
[Given: μ₀ = 4π × 10⁻⁷ T m/A]