# Calculation of Change in Magnetic Flux Linkage Across a Wire

• UnknownGuy
In summary, the solution to the given problem involves using Faraday's law to determine the induced e.m.f. across the ends of a wire that is moving at a steady speed in a magnetic field. This is done by considering an imaginary rectangular loop behind the wire and using the rate of change of the area covered by the flux, which can be positive or negative. However, it is safer to use the Blv law, which is based on the Lorentz force, to calculate the induced e.m.f. in moving media.
UnknownGuy

## Homework Statement

A straight wire of length 0.20m moves at a steady speed of 3.0m/s at right angles to a magnetic filed of flux density 0.10T. Use Faraday's law to determine the e.m.f. induced across the ends of a wire.

## Homework Equations

E= Nd Φ/dt but N=1 so E= dΦ/dt

## The Attempt at a Solution

The solution offered in the book:

Φ=BA
dΦ = BdA
dΦ/dt=B*dA/dt
dΦ/dt=0.10*Area moved by the length of the wire in 1 second (??)
dΦ/dt=0.10*3.0*0.20=0.06

E=0.06V

Now I understand that since the conductor is moving in a magnetic field, electrons experience a force and a charge separation occurs giving rise to an e.m.f. across the wire... By Faraday's law, this e.m.f. is equal (in this case) to dΦ/dt but here's the problem... I do not see how a wire cutting a uniform magnetic field experiences a change in magnetic flux. Its area is constant and magnetic flux density is constant so the magnetic flux felt by the wire Φ=BA is constant. The solution used the area covered by the wire which seems to me very irrelevant.

Faraday refers to a loop, not a piece of wire. Draw an imaginary rectangular loop behind the wire, with the other end of the loop not in the B field, to get the answer using Faraday. dA/dt is the rate of change of the area in the loop covered by the flux. It can be + or -.

Actually, using Faraday with moving media such as your wire is dangerous. Better to use the Blv law based on the Lorentz force q v x B:
emf = Blv, l = length of wire, v = velocity of wire. Forget about loops.

rude man said:
Faraday refers to a loop, not a piece of wire. Draw an imaginary rectangular loop behind the wire, with the other end of the loop not in the B field, to get the answer using Faraday. dA/dt is the rate of change of the area in the loop covered by the flux. It can be + or -.

Actually, using Faraday with moving media such as your wire is dangerous. Better to use the Blv law based on the Lorentz force q v x B:
emf = Blv, l = length of wire, v = velocity of wire. Forget about loops.
I understand. Thank you sir

## 1. How is magnetic flux linkage across a wire calculated?

The magnetic flux linkage across a wire can be calculated using the formula Φ = BAcosθ, where Φ is the magnetic flux, B is the magnetic field strength, A is the area of the wire, and θ is the angle between the magnetic field and the normal to the wire's surface.

## 2. What is the unit of measurement for magnetic flux linkage?

The unit of measurement for magnetic flux linkage is the weber (Wb) in the International System of Units (SI). It is also commonly expressed in terms of milliwebers (mWb) or microwebers (μWb).

## 3. Can the magnetic flux linkage across a wire change?

Yes, the magnetic flux linkage across a wire can change if there is a change in the magnetic field strength, the area of the wire, or the angle between the wire and the magnetic field. It can also change if the wire moves in relation to the magnetic field or if the magnetic field itself changes.

## 4. What factors can affect the calculation of magnetic flux linkage across a wire?

The calculation of magnetic flux linkage across a wire can be affected by the magnetic field strength, the area of the wire, the angle between the wire and the magnetic field, and any changes in these factors. It can also be affected by the material of the wire, as different materials have different magnetic properties.

## 5. How is the direction of the magnetic flux linkage determined?

The direction of the magnetic flux linkage is determined by the direction of the magnetic field and the direction of the current in the wire. The right-hand rule can be used to determine the direction of the magnetic flux, where the thumb points in the direction of the current, and the fingers curl in the direction of the magnetic field.

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