Question

A small sphere of mass $m=2gm$having charge $Q=5\mu C$ is suspended using an insulated string as shown in figure. The angle $Ɵ$ made by the sphere with vertical if it is placed in an electric field of magnitude $2000V/m$ towards right is

• A. ${\tan }^{-1}\left(5\right)$
• B. ${\tan }^{-1}(0.5)$
• C. ${\tan }^{-1}\left(2\right)$
• D. ${\tan }^{-1}(0.2)$

Answer 1

The correct option is B

${\tan }^{-1}(0.5)$

Step 1. Given data:

Mass of sphere, $m=2gm=0.002kg$

Charge on the sphere, $Q=5\mu C$

The magnitude of the electric field, $E=2000V/m$

Step 2. Finding the Angle made with verticle axis:

The force on the sphere due to the Electric field is $F=QE$ acting along$x$ axis

Force along $Y$ axis is $F=mg$

The angle is $\tan \theta =\frac{QE}{mg}$

$\tan \theta =\frac{5\times {10}^{-6}\times 2000}{0.002\times 10}$

$\tan \theta =0.5$

$\theta ={\tan }^{-1}\left(0.5\right)$

Hence, the correct option is B.