Respuesta :
The question is not clear.
Complete question is;
A circular coil of 14 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
(c) n = (i + j)/√2 Wb
(d) n = k Wb
(e) n = 0.7 i + 0.714142842854285 j Wb
Answer:
A) Electric flux = 0.044Wb
B) Electric flux = 0 Wb
C) Electric flux = 0.031 Wb
D) Electric flux = 0 Wb
E) Electric flux = 0.0308 Wb
Explanation:
equation for magnetic flux is given as;
Φ = NBAcosθ
where;
Φ is the magnetic flux
θ is the angle between n and B
N is the number of turns of wire.
A is the area.
Now,
N = 14 turns
Radius(r) = 5cm = 0.05 m
Area(A) = πr² = π x 0.05² =0.007854 m²
Magnetic field (B) = 4000G = 0.4 T
A) we are given the vector n = i Wb
Thus following the pattern of i + j used, where the number attached to j is y-value while that attached to i is x-value. So, y/x = tanθ
So, θ = tan^-1(y/x)
In this case, there is no j, so y = 0 and x = 1. so,
tanθ = 0/1 = 0 ;θ = tan^-1(0) =0
Thus,
Φ = NBAcosθ = 14 x 0.4 x 0.007854 x cos 0 = 0.044Wb
B)we are given the vector n = i Wb
Following the pattern in the above,
tan(θ) = 1/0
This doesn't exist and thus, magnetic flux = 0Wb
C) we are given the vector;
n = (i + j)/√2 Wb
So, Following the pattern in the first example,
tan(θ) = (1/√2)/(1/√2) = 1
θ = tan^-1(1) =45°
Thus,
Φ = NBAcosθ = 14 x 0.4 x 0.007854 x cos 45 = 0.031 Wb
D) n = k Wb
K is a neutral vector and as such Φ = 0
E) we are given;
n = 0.7 i + 0.714142842854285 j Wb
So, Following the pattern in the first example,
tan(θ) = (0.714142842854285)/(0.7) = 1.0202
θ = tan^-1(1.0202) =45.57°
Thus,
Φ = NBAcosθ = 14 x 0.4 x 0.007854 x cos 45.57 = 0.0308 Wb
