Question

A charge of magnitude '2e' and mass '4m' is moving in an electric field $\vec{E}$. The acceleration imparted to the above charge is

• A. $\frac{2m}{3Ee}$
• B. $\frac{Ee}{2m}$
• C. $\frac{2Ee}{3m}$
• D. $\frac{3m}{2Ee}$

Hint:

The simple base equation for acceleration inside an electric field is $a = \frac{qE}{m}$. Since the charge is doubled ($\times 2$) but the mass is quadrupled ($\times 4$), the base value gets scaled by a factor of $\frac{2}{4} = \frac{1}{2}$. This leads you directly to $\frac{Ee}{2m}$ without writing out lines of scratch work!

Answer 1

The Correct Option is B

Step 1: Find the force.
The charge $2e$ in field $E$ feels a force $F=qE=2eE$.

Step 2: Apply Newton's second law.
Acceleration is force over mass, and the mass is $4m$. \[ a=\frac{2eE}{4m} \]

Step 3: Simplify.
\[ a=\frac{eE}{2m}=\frac{Ee}{2m} \] \[ \boxed{\frac{Ee}{2m}} \]