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 [2 points] 0 attempt(s) made (maximum allowed for credit = 5) [after that, multiply credit by 0.5 up to 10 attempts] (b) n = j Wb [2 points] 0 attempt(s) made (maximum allowed for credit = 5) [after that, multiply credit by 0.5 up to 10 attempts] (c) n = (i + j)/square root of 2 Wb [2 points] 0 attempt(s) made (maximum allowed for credit = 5) [after that, multiply credit by 0.5 up to 10 attempts] (d) n = k Wb [2 points] 0 attempt(s) made (maximum allowed for credit = 5) [after that, multiply credit by 0.5 up to 10 attempts] (e) n = 0.7 i + 0.714142842854285 j Wb

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

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