Question

Inside an inkjet printer a tiny ball of mass 1.1 x 10^-11 ?? with charge −6.7 x 10^-12 ? moves horizontally with an initial velocity of 40 ?/? . The plates are used to deflect the ink ball, so that it lands on a particular spot on a piece of paper.

What electric field (magnitude and direction) should be applied to cause the ball to travel in a completely straight line?

Answer 1

Mass of ball $m=1.1*10^{-11}\,kg$

Charge of ball $q=-6.7*10^{-12}\,C$

Initial Velocity $v=40\,m/s$ horizontal

If the ball has to move in a straight line, net force on the ball must be zero.

Gravitational force on the ball $F_g= mg$ vertically downwards

Electric force on the ball $\vec{F}_e= q\vec{E}$

Since the net force is zero, $F_e= F_g$ with electric force vertically upwards.

$\vec{F}_e= q\vec{E}$ Since the charge is negative, electric field $\vec{E}$ is vertically downwards.

Magnitude of electric field is $|\vec{E}|=\frac{mg}{|q|}=\frac{1.1*10^{-11}*9.81}{6.7*10^{-12}}=16.1\,N/C$