The laws of electromagnetic induction (Faraday's and Lenz's law) are summarized in the following equation

An electron moves in the $$X$$-$$Y$$ plane with a speed of $${10^6}\,\,m/s.$$ Its velocity vector makes an angle of $${60^ \circ }$$ with $$X$$ axis. A magnetic field of magnitude $${10^{ - 2}}T$$ exists along the $$Y$$ axis. Compute the magnetic force exerted on the electron and its direction.

The Laplace transform of $$\,\left( {{t^2} - 2t} \right)\,u\left( {t - 1} \right)$$ is ______________.

The value of $$\,\,\,\int\limits_1^2 {{1 \over x}\,\,\,dx\,\,\,\,} $$ computed using simpson's rule with a step size of $$h=0.25$$ is