Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020PhysicsElectromagnetic InductionPractice

A conducting ring of circular cross-section with inner and outer radii a and b is made out of a material of resistivity ρ . The thickness of the ring is h . It is placed coaxially in a vertical cylindrical region of a magnetic field B = krt , where k is a positive constant, r is the distance from the axis and t is the time. If the current through the ring is I = kh αp b 3 - a 3 , then what is the value of α ?

Correct answer

9

Step-by-step solution

The flux through the area of radius r is ϕ = ∫ 0 r k r t 2 π r d r = 2 π k t r 3 3   E.M.F. induced, ϵ = dϕ dt = 2 πkr 3 3 Net induced current is I = ∫ a b 2 πr 3 khdr 3 ρ 2 πr = kh 9 ρ   b 3 - a 3 ∴      α = 9

Practice Electromagnetic Induction on Quantrex Academy →

More from Electromagnetic Induction

List-I contains four conducting loops lying in the XY plane, as shown in the figures. The loops are rotating about Z axis passing through the point O with time period T in clockwis 2026A 30 cm long solenoid has 10 turns per cm and area of 5 cm ^2 . The current through the solenoid coil varies from 2 A to 4 A in 3.14 s. The e.m.f. induced in the coil is 10⁻⁵ V. Th 2026A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as B = 0.4 (300t) Tesla. The normal to the plane of loop makes an angle of 60° with the field. 2026An inductor of inductance 10 mH having resistance of 100 , is connected to battery of E.M.F. 1.0 V through a switch as shown in the figure below. After switch is closed, the ratio 2026A metal rod of length L rotates about one end at origin with a uniform angular velocity . The magnetic field radially falls off as B(r) = B₀ e^ - r ; being a positive constant. The 2026A circular loop of radius 20 cm and resistance 2 is placed in a time varying magnetic field B = (2t^2 + 2t + 3) T . At t = 0 , for the plane of the loop being perpendicular to the 2026In the given circuit below inductance values of L₁ , L₂ and L₃ are same. The magnetic energy stored in the entire circuit is (U_t) and that stored in the L₂ inductor is (U_l) . U_t 2026A circular current loop of radius R is placed inside square loop of side length L(L >> R) such that they are co-planar and their centers coincide. The permeability of free space is 2026 Full Electromagnetic Induction list All NTA Abhyas JEE Main PYQs