A circular coil of 18 turns of radius 5 cm is in a uniform magnetic field of 400
ID: 2258576 • Letter: A
Question
A circular coil of 18 turns of radius 5 cm is in a uniform magnetic field of 4000 G in the positive x direction. Find the flux through the coil for the following orientations of the unit vector n that is perpendicular to the plane of the coil.
(a) n = i
( )Wb
(b) n= j
( )Wb
( )Wb
(d) n=k
( )Wb
(e) n = 0.8 i + 0.6 j
( )Wb
A circular coil of 18 turns of radius 5 cm is in a uniform magnetic field of 4000 G in the positive x direction. Find the flux through the coil for the following orientations of the unit vector n that is perpendicular to the plane of the coil.Explanation / Answer
Flux Phi=A(B.n), Where n is the normal vector to the area or Area vector
A=pi x r^2=(3.14x0.05^2)=0.00785 m^2
B=4000 G=4000x10^-4 T=0.4 T
a) Flux = AB ( Because B = Bi, n=i and i.i=1)
= 0.00785X 0.4
= 0.00314 Wb
b) Flux = 0 ( Because i.j=0)
c) Flux = AB/sqrt(2) (Because B.n= i.i/sqrt(2)=1/sqrt(2) )
= 0.00314/1.414
= 0.0022 Wb
d) Flux = 0 ( Again here i.k=0)
e) Flux = AB(0.8) ( here B.n=i.(0.8 i+ 0.6j)=0.8)
= 0.00314X0.8
= 0.002512 Wb
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