At a certain place, Earth's magnetic field has magnitude B =0.703 gauss and is inclined downward at an angle of 75.4° to the horizontal. A flat horizontal circular coil of wire with a radius of 10.0 cm has 1300 turns and a total resistance of 99.4 Ω. It is connected to a meter with 202 Ω resistance. The coil is flipped through a half-revolution about a diameter, so that it is again horizontal. How much charge flows in coulombs through the meter during the flip?

Respuesta :

Answer:

The charge flows in coulombs is

[tex]dq=1.843x10^{-5}C[/tex]

Explanation:

The current magnitude of current is given by the resistance and the induced Emf as:

[tex]I=N*\frac{dF}{Rdt}[/tex]

[tex]\frac{dq}{dt}=\frac{dF}{Rdt}=dq=N*\frac{dF}{R}[/tex]

[tex]dq=\frac{N*\beta*A*(Cos(\alpha_f)-Cos(\alpha_i}{R}[/tex]

[tex]N=1300[/tex], [tex]\beta=0.703[/tex], [tex]A=\pi*r^2=\pi*0.10^2=0.01\pi m^2[/tex], [tex]R=99.4+202=301.4[/tex]Ω

[tex]\alpha_f=14.6[/tex],[tex]\alpha_i=165.4[/tex]

Replacing :

[tex]dq=\frac{1300*0.703x10^{-4}*0.01\pi*(0.9667-(-0.9667))}{202+99.4}[/tex]

[tex]dq=1.843x10^{-5}C[/tex]