The following figure shows a conducting disc rotating about its axis in a perpendicular magnetic field B . The resistor of resistance R is connected between the centre and the rim. The current in the resistor is (The radius of the disc is 5.0 cm , angular speed ω =10 rad s- 1, B=0.40 T and R=10 Ω )

Question

The following figure shows a conducting disc rotating about its axis in a perpendicular magnetic field B . The resistor of resistance R is connected between the centre and the rim. The current in the resistor is (The radius of the disc is 5.0 cm , angular speed ω =10 rad s- 1, B=0.40 T and R=10 Ω ) <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-epmdp35vvaxy.png" /> (A) 0.5 A (B) 0.2 A (C) 0.3 A (D) 0.9 A

Tardigrade Admin · Accepted Answer

Emf induced between centre and rim ϵ =(Î ω a2/2), wherea=radius ∴ i=(ϵ /R)=(B ω a2/2 R)=(0.4 × 10 × (5 × 1 0- 2)2/2 × 10)=0.5A

$0.5 A$

$0.2 A$

$0.3 A$

$0.9 A$

Emf induced between centre and rim
$ϵ = \frac{B ω a ^{2}}{2}, w h ere a = r a d i u s$
$∴ i = \frac{ϵ}{R} = \frac{B ω a ^{2}}{2 R} = \frac{0.4 \times 10 \times ( 5 \times 1 0 ^{- 2} ) ^{2}}{2 \times 10} = 0.5 A$

Q. The following figure shows a conducting disc rotating about its axis in a perpendicular magnetic field B . The resistor of resistance R is connected between the centre and the rim. The current in the resistor is (The radius of the disc is 5.0cm , angular speed ω=10rads−1,B=0.40T and R=10Ω )

0.5A

0.2A

0.3A

0.9A

Emf induced between centre and rim ϵ=2Bωa2​,wherea=radius ∴i=Rϵ​=2RBωa2​=2×100.4×10×(5×10−2)2​=0.5A

$0.5 A$

$0.2 A$

$0.3 A$

$0.9 A$

Emf induced between centre and rim
$ϵ = \frac{B ω a ^{2}}{2}, w h ere a = r a d i u s$
$∴ i = \frac{ϵ}{R} = \frac{B ω a ^{2}}{2 R} = \frac{0.4 \times 10 \times ( 5 \times 1 0 ^{- 2} ) ^{2}}{2 \times 10} = 0.5 A$