Q 11-03-008NEETJEE MainEAMCET 2007 (Engineering)Easy
Velocity and acceleration vectors of a charged particle moving perpendicular to the direction of a magnetic field at a given instant of time are $\vec{v} = 2\hat{i} + c\hat{j}$ and $\vec{a} = 3\hat{i} + 4\hat{j}$ respectively. Then the value of $c$ is
Answer: (C) $-1.5$
The magnetic force $q\vec{v}\times\vec{B}$ is always perpendicular to the velocity, so the acceleration it produces is perpendicular to $\vec{v}$:
$$\vec{v}\cdot\vec{a} = 0 \;\Rightarrow\; 2(3) + c(4) = 0 \;\Rightarrow\; c = -1.5$$
Solution by Sreeraj P, M.Sc Physics