Question

Above, a negatively charged particle is pictured, moving northeast through a magnetic field that points straight up.
What is the direction of the force on the negatively charged particle at the moment it is pictured?

• A. Northeast
• B. Southeast
• C. Southwest
• D. Northwest
• E. Up

Answer 1

The correct option is D Northwest

From figure, $\overrightarrow{B}=B\hat{z}$ $\overrightarrow{v}=v_1\hat{x}+v_2\hat{y}$

Magnetic force $\overrightarrow{F}=-q(\overrightarrow{v}\times \overrightarrow{B})$

$\therefore$ $\overrightarrow{F}=-q\left[\right(v_1\hat{x}+v_2\hat{y})\times B\hat{z}]$

OR $\overrightarrow{F}=-qB\left[v_1\right(\hat{x}\times \hat{z})+v_2(\hat{y}\times \hat{z}\left)\right]$

OR $\overrightarrow{F}=-qB\left[v_1\right(-\hat{y})+v_2(\hat{x}\left)\right]$ $⟹$ $\overrightarrow{F}=qB[-v_2\hat{x}+v_1\hat{y}]$ i.e Northwest direction.