$9.1.1.$ A force of 15 N acts on a linear conductor of length $10$ cm, located perpendicular to a magnetic field, if the current in the conductor is $1.5$ A. Find the induction of the magnetic field.
We find the Ampere force as $$ \vec{F} = (\vec{Il})\times \vec{B} $$ In scalar form, this expression can be rewritten as $$ F = B\cdot Il \cdot \sin\alpha\quad(1) $$ since the field is perpendicular to the current element, then $$ \alpha =90^{\circ};\quad \sin\alpha =1 $$ From here, we rewrite the expression $(1)$ as $$ F = B \cdot Il \Rightarrow \boxed{B = \frac{F}{Il} = 100\text{ T}} $$
$$B = \frac{F}{Il} = 100\text{ T}$$