$9.1.2.$ A charge of $1$ C moving at a speed of $1 \text{ m/s}$ in a magnetic field is acted upon by a force of $10$ N. The charge moves at an angle of $30^{\circ}$ to the direction of the magnetic field induction. What is the induction of this field?
Lorentz force acting on a moving particle in a magnetic field $$ \vec{F} = q(\vec{v}\times \vec{B}) $$ rewriting in scalar form we get $$ F = qvB\sin\alpha $$ where $\alpha$ is the angle between $\vec{B}$ and $\vec{v}$
Substituting the values from the condition, we get $$ \boxed{{B} = \frac{F}{qv \sin\alpha} = 20 \text{ T}} $$
$${B} = \frac{F}{qv \sin\alpha} = 20 \text{ T}$$