Motional EMF [Part-I]

Magnetic flux changes as a loop moves into a magnetic field

Magnetic flux changes as a loop rotates in a magnetic field

Magnetic field strength (B), area (A), and orientation (angle θ)

Magnetic flux depends on what 3 factors?

Magnetic Flux Increases

What is the effect of the loop entering the magnetic field?

Magnetic flux changes with angle θ

What is the effect of the loop being rotated in the magnetic field?

MNOP circuit (N)

(i)

MNOP circuit (O)

(ii)

MNOP circuit (P)

(iii)

MNOP circuit (M)

(iv)

I

(v)

F_a

(vi)

v

(vii)

R

(viii)

l

(ix)

x

(x)

B

(xi)

F_m

(xii)

Φ_m = B × l × x

Magnetic flux for moving conductive rod formula

v = d(x)/dt

Velocity relation for moving conducting rod

ε = B × l × v

Induced EMF formula for moving conducting rod.
Also the result of analyzing the closed loop.

I = (Blv)/R

Current formula for the conductive moving rod.

No, Faraday’s law applies to any change in flux

Does Faraday’s law apply only to changing B?

Changing magnetic field, motion, or combination of both

Sources of flux change

P = (F_a) × v

Applied power for a moving conducting rod

F_m = I × l × B

Magnetic force on conductive moving rod

F_a = F_m

Condition for constant velocity in a conductive moving rod

(F_a)v = ((l^2)×(B^2)×(v^2))/R

Power produced by a conductive moving rod formula

P = (I^2)R = ((l^2)×(B^2)×(v^2))/R

Power dissipated in resistor by the moving conductive rod formula

Produced power = dissipated power (energy conservation)

Key principle seen inside the moving conductive rod example

Current

(1)

Magnetic field generated by current in rails

(2)

Armature and projectile accelerated forward by magnetic force

(3)

Projectile

(4)

Rails

(5)

Armature

(6)

Magnetic field interacts with current in armature, generating force

(7)

Electromagnetic launcher using current & magnetic field

What is a rail gun?

Current in rails → magnetic field → force on projectile

How does the Rail Gun works?

F = I × l × B

Key force formula for the Rail Gun Application

Requires extremely high current (around 10^6 A)

Limitation of Rail Gun application

Yes

Can emf exist without closed circuit?

By using imaginary loop and Faraday’s Law

How to analyze the closed circuit?

ε = 150μV

Typical motional EMF in Earth’s field (which is very small). Provide one example value

F = I×l×B×sin(θ)

Magnetic force formula

Ionosphere

The layer of the earth's atmosphere that contains a high concentration of ions and free electrons and is able to reflect radio waves. It lies above the mesosphere and extends from about 50 to 600 miles (80 to 1,000 km) above the earth's surface.

Tethered satellites

(१)

B_earth

(२)

Return path through ionosphere

(३)