Recall the standard expressions for force on a charge $q$:

• Electrostatic force: $\vec{F}_1 = q\vec{E}$

• Magnetic force on a charge moving with velocity $\vec{v}$: $\vec{F}_2 = q(\vec{v} \times \vec{B})$

Now check each option:

Option A: $\vec{F}_1 = q\vec{B}, \quad \vec{F}_2 = q(\vec{B} \times \vec{v})$

• First expression is wrong because electrostatic force depends on $\vec{E}$, not $\vec{B}$.
• Hence, A is incorrect.

Option B: $\vec{F}_1 = q\vec{V} \cdot \vec{E}, \quad \vec{F}_2 = q(\vec{B} \cdot \vec{V})$

• These are dot products, giving scalars, whereas force is a vector.
• Hence, B is incorrect.

Option C: $\vec{F}_1 = q\vec{E}, \quad \vec{F}_2 = q(\vec{V} \times \vec{B})$

• This exactly matches the standard formulas.
• Hence, C is correct.

Option D: $\vec{F}_1 = q\vec{E}, \quad \vec{F}_2 = q(\vec{B} \times \vec{V})$

• Since cross product is anti-commutative, $\vec{B} \times \vec{V} = -(\vec{V} \times \vec{B})$
• So this gives the opposite direction of magnetic force.
• Hence, D is incorrect.

Final Answer: $\boxed{\text{Option C}}$

Comparison with stored correct answer:

• Stored correct answer: C
• Derived answer: C
• They match.