Ampere's Law — Applications (solenoid, toroid)
Magnetic Effects of Current
13
JEE Qs
8%
Hard
60
min
Master the Amperian loop selection and accurate calculation of enclosed current (I_enc) for symmetric current distributions.
🧮 Key Formulas
✅ Key Points for JEE
- 1The primary skill is judiciously choosing an Amperian loop that exploits the symmetry of the magnetic field (where B is constant and parallel to dl, or perpendicular to dl, or zero).
- 2For an ideal long solenoid, the magnetic field is uniform and axial inside, and negligibly small outside. The derivation uses a rectangular Amperian loop.
- 3For an ideal toroid, the magnetic field is entirely confined within the toroid core, circulating along its circumference, and zero in the empty space inside and outside the toroid. The derivation uses a circular Amperian loop.
- 4Carefully determine the 'I_enc' (net current enclosed by the Amperian loop), considering the number of turns (N for toroid, n for solenoid) and the direction of current flow.
⚠️ Common Mistakes
- ✕Incorrectly selecting the Amperian loop, leading to complex integrals instead of simplification, or an invalid application of the law.
- ✕Errors in calculating the enclosed current (I_enc), often confusing total turns (N) with turns per unit length (n) or miscounting the current piercing the loop.
- ✕Assuming Ampere's Law applies universally without considering the underlying condition of steady currents or ignoring the integral form and directly applying simplified formulas without context.
📝 Practice Questions
See allQ43.Match List - I with List - II. List - I List - II (A) Magnetic induction (I) Ampere meter 2 (B) Magnetic intensity (II) Weber (C) Magnetic flux (III) Gauss (D) Magnetic moment (IV) Ampere/meter (1) (A)-(I), (B)-(II), (C)-(III), (D)-(IV) (2) (A)-(III), (B)-(IV), (C)-(I), (D)-(II) (3) (A)-(III), (B)-(II), (C)-(I), (D)-(IV) (4) (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
Q46.The magnetic field inside a 200 turns solenoid of radius 10 cm is 2.9 × 10−4Tesla. If the solenoid carries a current of 0.29 A , then the length of the solenoid is ________ πcm .
Q47.A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is 7 × 108 V/s then the integer value of the distance between the parallel plates is ( Take, ϵ0 = 9 × 10−12 mF , π = 227 ) ________ μm . 2025 (29 Jan Shift 2) JEE Main Previous Year Paper
Q37.If B is magnetic field and μ0 is permeability of free space, then the dimensions of (B/μ0) is (1) ML2 T−2 A−1 (2) MT−2 A−1 (3) L−1 A (4) LT−2 A−1
Q46.A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of 2 × 105 ms−1 . When the electric field is switched off, the proton moves along a circular path of radius 2 cm . The magnitude of electric field is x × 104 N/C. The value of x is _______ Take the mass of the proton = 1.6 × 10−27 kg.
Q50.Two long parallel wires X and Y , separated by a distance of 6 cm , carry currents of 5A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance 2025 (22 Jan Shift 2) JEE Main Previous Year Paper of 4 cm from wire Y is x × 10−5 T. The value of x is__________ . Take permeability of free space as μ0 = 4π × 10−7SI units.
NCERT Chapters
- Class 12 Physics Part 1 Ch 4: Moving Charges and Magnetism