The magnetic flux through a coil perpendicular to its plane and directed into paper is varying according to the relation φ=(2t2+4t+6) m Wb The emf induced in the loop at t = 4 s is

Question

The magnetic flux through a coil perpendicular to its plane and directed into paper is varying according to the relation φ=(2t2+4t+6) m Wb The emf induced in the loop at t = 4 s is (A) 0.12 V (B) 2.4 V (C) 0.02 V (D) 1.2 V

Tardigrade Admin · Accepted Answer

Given, φ = (2t2+4t+6)m wb As, ε=(dφ/dt)=(d/dt) (2t2+4t+6) m Wb s-1 =(4t+4)× 10-3 V At t=4 s ε =(4×4+4)×10-3 V =20×10-3 V =0.02 V

Q. The magnetic flux through a coil perpendicular to its plane and directed into paper is varying according to the relation $ϕ = (2 t^{2} + 4 t + 6) m Wb$ The emf induced in the loop at $t = 4 s$ is

$0.12 V$

$2.4 V$

$0.02 V$

$1.2 V$

Given, $ϕ = (2 t^{2} + 4 t + 6) m w b$
As, $ε = \frac{d ϕ}{d t} = \frac{d}{d t} (2 t^{2} + 4 t + 6) m Wb s^{- 1}$
$= (4 t + 4) \times 1 0^{- 3} V$
At $t = 4 s$
$ε = (4 \times 4 + 4) \times 1 0^{- 3} V$
$= 20 \times 1 0^{- 3} V$
$= 0.02 V$

Q. The magnetic flux through a coil perpendicular to its plane and directed into paper is varying according to the relation ϕ=(2t2+4t+6)mWb The emf induced in the loop at t=4s is

0.12V

2.4V

0.02V

1.2V