A conducting circular loop made of a thick wire, has area 3.5 × 10-3 m2 and resistance 10 Ω . It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T) sin(50 π t). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to:

Question

A conducting circular loop made of a thick wire, has area 3.5 × 10-3 m2 and resistance 10 Ω . It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T) sin(50 π t). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to: (A) 0.14 mC (B) 21 mC (C) 6 mC (D) 7 mC

Tardigrade Admin · Accepted Answer

Q = (Δ φ/R) = (1/10) A(Bf -Bi) = (1/10) ×3.5 ×10-3 (0.4 sin (π/2) -0) = (1/10) (3.5 ×10-3)(0.4 - 0) = 1.4 ×10-4 = 0.14 mC

Q. A conducting circular loop made of a thick wire, has area 3.5×10−3m2 and resistance 10Ω . It is placed perpendicular to a time dependent magnetic field B(t)=(0.4T)sin(50πt). The field is uniform in space. Then the net charge flowing through the loop during t=0s and t=10ms is close to:

0.14 mC

21 mC

6 mC

7 mC

Q=RΔϕ​=101​A(Bf​−Bi​)=101​×3.5×10−3(0.4sin2π​−0) =101​(3.5×10−3)(0.4−0) =1.4×10−4=0.14mC

$Q = \frac{Δ ϕ}{R} = \frac{1}{10} A (B_{f} - B_{i}) = \frac{1}{10} \times 3.5 \times 1 0^{- 3} (0.4 sin \frac{π}{2} - 0)$
$= \frac{1}{10} (3.5 \times 1 0^{- 3}) (0.4 - 0)$
$= 1.4 \times 1 0^{- 4} = 0.14 m C$