How Did Ampere and Kirchhoff Shape Modern Electromagnetism?

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Andre-Marie Ampere is known for formulating Ampere's Law, which describes the relationship between electric current and magnetic fields, laying the groundwork for electromagnetism. His experiments involved measuring the force between current-carrying wires, leading to the understanding of magnetic fields generated by electric currents. Gustav Kirchhoff contributed significantly with his laws of circuit analysis, which help in understanding current and voltage in electrical circuits. His work on the conservation of charge and energy in electrical networks is foundational for modern electrical engineering. Both scientists' discoveries have directly influenced contemporary technologies, such as electric motors and circuit design.
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I need help with these scientists:

THIS ALL HAS TO RELATE TO ELECTROMAGNETISM

What did they discover (and a quick summary)
How did they discover it (what experiment did they have to go through)
What current invention has been based on what this person has discovered

The scientists:

Andre-Marie Ampere
Gustav Kirchhoff
 
Physics news on Phys.org
sorry about redirecting you.

but i think a quick wikipedia or google search should get you your info
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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