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A circular coil has a 7.85 cm radius and consists of 36.0 closely wound turns of wire. An externally produced magnetic field of magnitude 2.95 mT is perpendicular to the coil. (a) If no current is in the coil, what magnetic flux links its turns

User Tiernan
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2 Answers

3 votes

Answer:

2.056 x 10⁻³ Wb

Step-by-step explanation:

The magnetic flux, Φ₀, through a single turn of a coil is given by the dot product between the magnetic field, B, and the area, A, of the coil. i.e

Φ₀ = B.A cos θ --------------(i)

Where;

θ = angle between the area vector and the magnetic field.

But for a coil with N number of turns, the magnetic flux, Φ₀, is actually the product of the number of turns and the magnetic flux through its single turn, Φ₀. i.e

Φ = N Φ₀ --------------(ii)

Substitute the value of Φ₀ in equation (i) into equation (ii) as follows;

Φ = N BAcosθ --------------(iii)

From the question, the coil is perpendicular to the magnetic field. This implies that the area vector is parallel to the magnetic field. Therefore equation (iii) becomes;

Φ = N BA ------------------(iv)

Also,

A = πr²

Where;

r = radius of the coil

Substitute A = πr² into equation (iv) as follows;

Φ = N B(πr²)

Φ = Nπr²B --------------(v)

From the question;

N = 36.0

r = 7.85cm = 0.0785m

B = 2.95mT = 2.95 x 10⁻³ T

Substitute these values into equation (v) as follows and take π = 3.142;

Φ = 36.0 x 3.142 x 0.0785² x 2.95 x 10⁻³

Φ = 0.002056

Φ = 2.056 x 10⁻³ Wb

Therefore, the magnetic flux linking its turns is 2.056 x 10⁻³ Wb

User Libardo
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4.5k points
5 votes

Answer:

Φ = 2.06×10^-3weber

Step-by-step explanation:

Magnetic flux density is the ratio of the flux links to the area of the coil.

This can be expressed as

B =Φ/NA where:

Φ is the magnetic flux

B is the magnetic field strength

A is the area of the coil.

N is the number of turn in the wire

Given

B = 2.95 mT = 2.95×10^-3T

N = 36

radius = 7.85cm = 0.0785m

A = πr² ( since it is a circular coil)

A = π(0.0785)²

A = 0.0194m²

From the formula Φ = BAN

Φ = 2.95×10^-3 × 0.0194×36

Φ = 2.06×10^-3weber

User Stradivari
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4.6k points