Brodie Beck

2022-10-02

Magnetic force comparison

Two magnets of different size are tied on two sides of a wall with non-elastic rope on a horizontal surface and the opposite poles face each other. Why is the tension on both of the ropes the same? Shouldn't the tension be greater on the smaller magnet?

Two magnets of different size are tied on two sides of a wall with non-elastic rope on a horizontal surface and the opposite poles face each other. Why is the tension on both of the ropes the same? Shouldn't the tension be greater on the smaller magnet?

Frida King

Beginner2022-10-03Added 8 answers

Let the tensions on the two ropes be ${T}_{1}$ and ${T}_{2}$, and let the magnetic forces on the two magnets have magnitude ${F}_{1}$ and ${F}_{2}$. Because the first and second magnet experience no net force,

${T}_{1}={F}_{1},\phantom{\rule{1em}{0ex}}{T}_{2}={F}_{2}.$

But by Newton's third law,

${F}_{1}={F}_{2}$

because the force of the first magnet on the second equals the force of the second magnet on the first; the two form an action reaction pair. So putting these equations together,

${T}_{1}={T}_{2}.$

The tensions on the ropes have to be equal.

${T}_{1}={F}_{1},\phantom{\rule{1em}{0ex}}{T}_{2}={F}_{2}.$

But by Newton's third law,

${F}_{1}={F}_{2}$

because the force of the first magnet on the second equals the force of the second magnet on the first; the two form an action reaction pair. So putting these equations together,

${T}_{1}={T}_{2}.$

The tensions on the ropes have to be equal.

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