1. The current I through a long solenoid with n turns per meter and radius 0.30m is changing with time as given by /=sin(120t). The magnetic field inside a solenoid is given by B=nuol where Ho is the free space permeability Ho=1.26-10-6 H/m. What is the magnetic flux through a single coil at a time of t= 1.1 s at distance r= 0.25 m from the center of the solenoid if there are, n=108 turns/m? a) Start by determining the flux through a gaussian loop of radius r=0.25 m centered in the middle of the solenoid. Hint: Is the angle for the sine function in degrees or radians? B=nuosin(120t) ²2²= VTm² b) Next determine the rate of change of the magnetic flux with time d (nuosin(120t)²) = Tm²/s dt $B= d dt |§E·a|-|-dd₂| Recall that the symmetry of the c) The electic field can then be determined from dt problem means the electric field is constant when integrating around the loop. E= V/m

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1. The current I through a long solenoid with n turns per meter and radius 0.30m is changing with time
as given by /=sin(120t). The magnetic field inside a solenoid is given by B=nuol where μo is the free
space permeability Ho=1.26-10-6 H/m.
What is the magnetic flux through a single coil at a time of t= 1.1 s at distance r= 0.25 m from the
center of the solenoid if there are, n=108 turns/m?
a) Start by determining the flux through a gaussian loop of radius r=0.25 m centered in the middle of
the solenoid. Hint: Is the angle for the sine function in degrees or radians?
B=nuosin(120t) ² =
VTm²
b) Next determine the rate of change of the magnetic flux with time
d
Tm²/s
dt
d
B=(nuosin(120t) π²) =
dt
| fe·a|=|de|
dt
Recall that the symmetry of the
problem means the electric field is constant when integrating around the loop.
E=
VV/m
c) The electic field can then be determined from
B
Transcribed Image Text:1. The current I through a long solenoid with n turns per meter and radius 0.30m is changing with time as given by /=sin(120t). The magnetic field inside a solenoid is given by B=nuol where μo is the free space permeability Ho=1.26-10-6 H/m. What is the magnetic flux through a single coil at a time of t= 1.1 s at distance r= 0.25 m from the center of the solenoid if there are, n=108 turns/m? a) Start by determining the flux through a gaussian loop of radius r=0.25 m centered in the middle of the solenoid. Hint: Is the angle for the sine function in degrees or radians? B=nuosin(120t) ² = VTm² b) Next determine the rate of change of the magnetic flux with time d Tm²/s dt d B=(nuosin(120t) π²) = dt | fe·a|=|de| dt Recall that the symmetry of the problem means the electric field is constant when integrating around the loop. E= VV/m c) The electic field can then be determined from B
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