Question

Problem 5 Calculate the magnetic field in the center of the circuit to the right if R1 = 612, R2 = 312 and € = 12 V Problem 6

Inner Radius = 5cm, Outer Radius= 10cm

Answer 1

R1 R2

R₁ and R₂ are in parallel and their parallel combination is given as

R = R₁ R₂/(R₁ + R₂) = (6) (3)/(6 + 3) = 2 ohm

E = battery voltage = 12 Volts

i = total current coming from the battery = E/R = 12/2 = 6 A

i₂ = current flowing in resistor R₂ = E/R₂ = 12/3 = 4 A

i' = = i - i₂ = 6 - 4 = 2 A

Magnetic field at the center is given as

B = ($\mu _{o}$/4$\pi$) (2 i) ($\pi$/2) (1/R_inner - 1/R_outer) + ($\mu _{o}$/4$\pi$) (2 i') ($\pi$) (1/R_inner - 1/R_outer)

B = (10^-7) (2 x 6) (1.57) (1/0.05 - 1/0.10) + (10^-7) (2 x 2) (3.14) (1/0.05 - 1/0.10)

B = 31.4 x 10^-6 T