Chapter 93: The First Cornerstone: Quantifying the Magnetic Field

Deep into the night, the capital outside his window was torn asunder by the muffled wails and the clang of patrol guards’ armor. The lamentations, born from shattered faith, grated against the eardrums of every awakened soul.

Faraday, however, was deaf to it all. In his world, there were only the three parchment sheets on his desk, meticulously covered in data.

Number of current sources versus deflection angle. Distance versus deflection angle. Number of coil turns versus deflection angle.

To others, these cold figures were nothing more than meaningless ink splotches, yet to Faraday, they were vibrant notes, a magnificent anthem poised to compose a new chapter for the cosmos!

His gaze settled on the magnetic needle, deflected by the current.

Miss Lia Farrien’s treatise had proclaimed to the world the revolutionary truth that ‘electricity generates magnetism.’ But this was not enough. Far from it!

Faraday’s fingertips traced over the data he had recorded, an inferno raging within his heart. Miss Lia Farrien, through a single phenomenon, had illuminated a path to a new world for everyone.

Yet, this very path was now steeped in blood and lamentation, for people only perceived its existence, unwilling to grasp its underlying rules, and thus, fear took root in their hearts.

‘How much ‘is there,’ precisely? How strong ‘can it be,’ truly?’

Her proclamation had merely, with supreme power, forced open a tightly sealed door. What he intended to do was precisely measure the entire world behind that door, quantified by the numbers of truth!

Faraday’s breathing remained steady, his eyes alight with the fervent flame of inquiry. He picked up his pen and began to inscribe his deductions onto a fresh sheet of parchment.

The deflection of the magnetic needle was caused by a force. This force originated from that invisible, intangible, yet undeniably real entity generated by the flowing charges in the conductor—the magnetic field.

He needed a symbol to define it. After a moment of contemplation, he solemnly penned a single letter, designating it to represent the strength of the magnetic field.

From the experiments, it was visually evident that a larger deflection angle indicated a stronger magnetic force.

Therefore, the first conclusion could be drawn: magnetic field strength is directly proportional to the angle of deflection.

Building on this, he turned his attention to the first data table.

When the distance remained constant, the greater the number of current sources and the stronger the current intensity, the larger the deflection angle. A perfect direct proportionality existed between them.

Since B∝θ, and θ∝I. Then, B∝I.

The strength of the magnetic field is directly proportional to the magnitude of the current generating it.

As a clear conclusion emerged, Faraday’s heart gave a sudden leap, and a thrill shot up his spine to the crown of his head. He forcefully suppressed this tremor, shifting his gaze to the second data table.

When the current remained constant, the greater the distance ‘r,’ the smaller the deflection angle ‘θ.’ This was an inverse relationship.

Therefore, B∝1/r.

The strength of the magnetic field is inversely proportional to the distance ‘r.’

With two conclusions laid before him, a grander law began to reveal its elegant yet austere outline within the mist. Faraday integrated them without hesitation.

A single line of simple symbols, yet possessing the immense power to explain the world!

Faraday’s chest heaved violently; he could almost hear the roar of his own blood coursing through his veins. He knew he was but one final step away from truth.

To transform this ambiguous proportionality into a computable equation! He introduced a constant, K.

B=K·I/r.

A perfect equation.

Yet, a new problem loomed before him like an insurmountable mountain. In this equation, for current intensity I, he could define the output of a standard alchemical battery as one unit.

Distance ‘r’ he could measure with a ruler. The constant K was the unknown that needed to be solved.

But how was the magnetic field strength B to be measured?

The deflection angle ‘θ’ was merely the result of the magnetic field’s effect; he couldn’t directly use an angle to represent the absolute numerical value of the magnetic field.

He needed a method, one capable of independently measuring the precise numerical value of magnetic field B.

Faraday fell into deep contemplation, the tide of excitement receding to leave behind the parched reefs of frustration.

He stood up and paced back and forth in the cramped room, his fingers unconsciously stroking his chin.

He needed a known and stable magnetic field as a yardstick. A benchmark! An anchor point! But where could such a magnetic field be found?

His gaze inadvertently flickered to the magnetic needle on the corner of the table, which served as a reference.

That black pointer, regardless of the clamor outside, always stubbornly pointed north when undisturbed by electric currents.

‘Pointing… North?’

Boom! A thought detonated in his mind, making his very soul hum with vibration! He abruptly halted, his eyes wide, as if seeing the world for the first time.

The Earth he stood upon. The ground beneath his feet. This world itself.

Was a magnet so colossal it defied imagination—the Earth’s magnetic field! An omnipresent, grand, and immense existence, yet one no one had ever thought to measure!

Faraday’s breathing instantly quickened, his eyes blazing with a frightening brilliance. He recalled Master Charles Coulomb that day…

That apparatus could measure faint gravitational forces, faint electric charges… Then, it surely could also measure equally faint magnetic forces!

Once inspiration erupted, it could no longer be contained.

Faraday lunged towards the space beneath his bed, rummaging through a wooden crate crammed with various components, unearthing his precious collection—a magnetic bar with a standard magnetic moment, officially crafted by the School of Magnetism, and a small coil of quartz filament finer than a strand of hair.

He was going to replicate Coulomb’s experiment! But this time, what he intended to measure was not the whispered interactions between two small spheres, but the very pulse of the planet beneath his feet!

He meticulously assembled the torsion balance and replaced its component with the standard magnetic bar. Beneath the torsion balance, he then positioned a graduated dial.

The principle of the experiment unfolded clearly in his mind. The Earth’s magnetic field would exert a torque on the magnetic bar, attempting to align it north-south.

The twisting of the quartz filament, in turn, would generate an opposing elastic torque.

When these two forces balanced, he could calculate the strength of the Earth’s magnetic field by observing the torsion angle of the quartz filament.

Holding his breath, he began the procedure. First, he allowed the magnetic bar to hang freely and come to rest on the torsion balance, its pointer indicating the north-south direction.

At this point, the magnetic torque was zero, and the quartz filament was untwisted.

Second, he rotated the top dial, forcing the quartz filament to twist, thereby rotating the magnetic bar away from the north-south alignment until it formed a ninety-degree angle with its initial position.

He held his breath and recorded the torsion angle shown on the top dial.

Third, the calculation. According to the law of elasticity formulated by the ancients, the elastic torque of the quartz filament’s torsion was equal to its torsion coefficient multiplied by the twisting angle.

He had already precisely measured this torsion coefficient by suspending small objects of known weight. The geomagnetic torque exerted on the magnetic bar was equal to the magnetic moment of the bar multiplied by the magnetic field strength and the sine of the angle between them.

The magnetic moment of the bar was a standard unit issued by the School.

When the two balanced, the elastic torque equaled the geomagnetic torque. Thus, the magnetic field strength equaled the elastic torque divided by the magnetic moment and the sine of the angle!

As Faraday, with his quill pen, calculated the precise numerical value of the Earth’s magnetic field strength on the parchment, his hands began to tremble uncontrollably.

He had done it. With a simple apparatus, he had quantified the invisible force that enveloped the entire world!

Now, all the pieces of the puzzle were assembled.

He returned to his initial battlefield. In this equation, current was his defined unit, distance was a value he measured with a ruler, and magnetic field strength could now be derived by converting the magnetic needle’s deflection angle with the Earth’s magnetic field strength he had just calculated!

The only unknown remaining was the constant K, representing a law of the universe.

Faraday selected three sets of data he had recorded, substituting them into the formula.

The first set of data, the second set of data, the third set of data—after accounting for the inaccuracies of his rudimentary instruments, the three results converged almost perfectly upon a single, minuscule number!

Finally, he took their average and solemnly wrote: [K value determined by Faraday’s calculation].

‘Haha… hahahaha!’

Faraday gazed at the three remarkably close numbers on the parchment, no longer able to suppress the ecstasy within him, and let out a deep, unrestrained laugh.

From this moment forward, this was no longer a mere conjecture, but an unyielding truth, capable of being repeatedly calculated and verified by anyone!

Calming his agitated heart, he unrolled a fresh, pristine sheet of parchment and began to write, emulating Miss Lia Farrien’s clear and rigorous essay format.

He titled his treatise—’On the Quantitative Laws of Steady Current Magnetic Fields.’

Abstract, Introduction, Experimental Apparatus, Innovative Method for Measuring Earth’s Magnetic Field Strength, Data and Analysis of Three Core Experiments, Final Formula and Calculation of the Constant…

After penning the final word, Faraday exhaled a long breath. He knew that this paper in his hands would ignite an even more ferocious new wave amidst the towering tempest already stirred.

Miss Lia Farrien, she had dislodged the foundations of the old era with a single phenomenon; she was the prophet of the storm. And he, Michael Faraday, would lay the first precisely calculable cornerstone for the new era with an equation!

He carefully rolled up the treatise and glanced out the window. The faint light of dawn pierced through the capital’s chaos, which seemed to have momentarily subsided.

The dim morning light gilded the city, freshly ravaged by catastrophe, with a false, tranquil golden edge.

He pushed open his door and, facing the faint morning light, headed towards the Magic Association.