A conducting circular loop of area 2.5× 10- 3m2 and resistance 10Ω is placed perpendicular to a time varying magnetic field B(.t.)=0.6Tsin(.50π t.). The field is uniform in space. The net charge flowing through the loop during t=0s and t=10ms is (k/2)mC . Find the value of k .

Question

A conducting circular loop of area 2.5× 10- 3m2 and resistance 10Ω is placed perpendicular to a time varying magnetic field B(.t.)=0.6Tsin(.50π t.). The field is uniform in space. The net charge flowing through the loop during t=0s and t=10ms is (k/2)mC . Find the value of k . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Net charge =(Δ φ/ R )=( A ( B 2- B 1)/ R ) =(2.5 × 10-3)(0.6)[ sin (50 π(10)/103)- sin 0] =1.5 × 10-3[ sin (π/2)- sin 0] =1.5 × 10-3 C =(3/2) mC

Q. A conducting circular loop of area 2.5×10−3m2 and resistance 10Ω is placed perpendicular to a time varying magnetic field B(t)=0.6Tsin(50πt). The field is uniform in space. The net charge flowing through the loop during t=0s and t=10ms is 2k​mC . Find the value of k .

Net charge =RΔϕ​=RA(B2​−B1​)​ =(2.5×10−3)(0.6)[sin10350π(10)​−sin0] =1.5×10−3[sin2π​−sin0] =1.5×10−3C=23​mC

Net charge $= \frac{Δ ϕ}{R} = \frac{A ( B _{2} - B _{1} )}{R}$
$= (2.5 \times 1 0^{- 3}) (0.6) [sin \frac{50 π ( 10 )}{1 0 ^{3}} - sin 0]$
$= 1.5 \times 1 0^{- 3} [sin \frac{π}{2} - sin 0]$
$= 1.5 \times 1 0^{- 3} C = \frac{3}{2} m C$