is all about creating electricity from changing magnetic fields. ###'s_Law_0### tells us that the always opposes the change causing it, like a stubborn friend who always does the opposite of what you want.
helps us calculate the induced voltage, while Lenz's law explains its direction. This dance between electricity and magnetism is key to understanding how generators work and why your phone charger gets warm.
Lenz's Law and Electromagnetic Induction
Direction of induced current
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Lenz's law states induced current in conductor opposes change in magnetic flux that caused it
When magnetic flux through loop increases, induced current flows to create magnetic field opposing increase in flux
When magnetic flux through loop decreases, induced current flows to create magnetic field opposing decrease in flux
Bar magnet's north pole moved towards coil, induced current flows to create magnetic field with north pole facing approaching magnet, repelling it
Bar magnet's north pole moved away from coil, induced current flows to create magnetic field with south pole facing receding magnet, attracting it
The can be used to determine the direction of the induced current
Calculation of induced emf
Faraday's law states magnitude of induced emf (E) in circuit directly proportional to rate of change of magnetic flux (ΦB) through circuit
For tightly wound coil with N turns, induced emf given by:
E=−NdtdΦB
Magnetic flux through coil or given by:
ΦB=BAcosθ
B magnetic field strength
A of coil or
θ angle between magnetic field and normal to coil's surface
Combining equations, induced emf in coil or solenoid calculated as:
E=−NAdtdBcosθ (if B changes with time)
E=−NABdtdcosθ (if angle θ changes with time)
E=−NBdtdAcosθ (if area A changes with time)
Lenz's law and energy conservation
Lenz's law consequence of conservation of energy principle
Induced current always flows in direction that opposes change in magnetic flux that caused it
Opposition ensures energy conserved in system
If induced current flowed in same direction as change in flux, it would amplify change, leading to ever-increasing flux and current, violating conservation of energy
By opposing change in flux, induced current acts to minimize overall change in system
Opposition converts some mechanical energy used to change flux into electrical energy in form of induced current
Work done by external force to overcome opposing force due to induced current equal to electrical energy generated in circuit
Demonstrates conservation of energy, as mechanical work converted into electrical energy
Magnetic Field Interactions
represent the direction and strength of a magnetic field in space
The created by the induced current interacts with the external magnetic field
The magnetic dipole moment of a current loop determines its interaction with external magnetic fields