Ampere's law: straight wire and solenoid
- From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is : Answer: 4. a linearly increasing function of distance r upto the boundary of the wire and then decreasing one with 1/r dependence for the ou... 1
- A long solenoid of radius 1 mm has 100 turns per mm. If 1 A current flows in the solenoid, the magnetic field strength at the centre of the solenoid is : Answer: 3. 12.56 × 10⁻² T Field at the centre of a long solenoid is B=μ₀ nI . n=100 turns/mm =10⁵ turns/m. B=4π×10⁻⁷×10⁵×1=0.1256\ T=12.56×1... 1
- A thick current carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by : Answer: 3. Graph (3): B vs r, linear rise to a peak then decreasing Key idea: use Ampere's law inside and outside the cable. Inside ( r Outs... 1
- A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is :(μ_0 = 4π×10^-7 T m A^-1) Answer: 1. 6.28×10⁻⁴ T Field inside a long solenoid: B=μ₀nI , with n turns per metre. n=100/0.5=200\ m⁻¹ B=4π×10⁻⁷×200×2.5=6.28×10⁻⁴\ T Answ... 1
- A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field, B with the distance, d, from the centre of the conductor, is correctly represented by the figure : Answer: 3. [graph] B increasing linearly for d < R, peak at R, then decreasing for d > R By Ampere's law for a cylindrical conductor with un... 1
- A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross - section. The ratio of the magnetic fields B and B', at radial distances a/2 and 2a respectively, from the axis of the wire is : Answer: 3. 1 Key idea: use Ampere's law. Inside the wire, B=μ₀Ir/2π a² ; outside, B=μ₀I/2π r . At r=a/2 : B=μ₀I/4π a . At r=2a : B'=μ₀I/4π a... 1