Respuesta :
Answer:
B(max) = 3.7971 × [tex]10^{-12}[/tex] T
Explanation:
given data
radius R = 26 mm
plate separation d = 4.0 mm
potential difference Vm = 220 V
frequency f = 76 Hz
V = (220 V) sin[2π(76 Hz)t]
solution
we know that E will be
E = V ÷ d ............1
put here value
E = [tex]\frac{220 \times sin(2\pi 76\times t)}{d}[/tex]
and here we take as given r = R
so A = π R² .................2
and
ФE = E × A
ФE = [tex]\frac{\pi R^2 \times 220 \times sin(2\pi 76 \times t)}{d}[/tex] .....................3
so use use here now Ampere's Law that is
∫ B ds = [tex]\mu_o \times \epsilon_o \times \frac{d\Phi E}{dt} + \mu_o \times I_{encl}[/tex] .....................4
and
here [tex]I_{encl}[/tex] is = 0 and r = R
so
[tex]2B \times \pi \times R = \mu_o \times \epsilon_o \times \frac{d\Phi E}{dt}[/tex] .....................5
and put here value we get
B = [tex]\frac{\mu_o \times \epsilon_o \times \pi \times f \times R \times V_m cos(2\pi f t)}{d}[/tex] .....................6
put here value for B maximum cos(2πft) = 1
and we get B (max)
B(max) = [tex]\frac{\mu_o\times \epsilon_o\times \pi \times f\times R\times V_m}{d}[/tex] ....................7
put here all value
B(max) = [tex]\frac{4\pi \times10^{-7} \times 8.85\times 10^{-12}\times \pi \times 76 \times 0.026\times 220 }{4\times 10^{-3}}[/tex]
solve it we get
B(max) = 3.7971 × [tex]10^{-12}[/tex] T
