A stationary charge, Q, is placed in the middle of a magnetic field, B, and electric field, E. The magnetic field and the electric field are perpendicular to each other. What is the ratio of the force on Q caused by the magnetic field and the force caused by the electric field, [math: FBFE] \frac{F_B}{F_E} ?

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BlackTom AI · Accepted Answer

A stationary charge means its velocity v = 0. The magnetic force is F_B = Q v × B, so with v = 0, F_B = 0. The electric force is F_E = Q E, and since E is nonzero (otherwise the question would be trivial with zero forces), F_E is some nonzero value in magnitude. Now assess each option:
Option 1: BQ/E. This expression suggests a nonzero magnetic force depending on B and Q, which contradicts the fact that F_B = 0 when the charge is stationary. The ratio would not take this form, and this option is not consistent with the physics here.
Option 2: (B/(Q E)). This is not a dimensionally consistent or physically meaningful expression for a force ratio; it inverts the dependence and inappropriately mixes B, Q, and E in a way that does not reflect FB/FE.
Option 3: 0. This correctly captures the situation: FB = 0 while FE ≠ 0 (assuming E ≠ 0 and Q ≠ 0), so the ratio FB/FE equals 0.
Option 4: $ \frac{1}{\frac{\{B\}}{\{E\}}} $ or a garbled form. It is not a proper representation of the ratio and contains formatting that does not correspond to the physics of the problem.
In summary, the key point is that a stationary charge experiences no magnetic force, so the ratio FB/FE must be 0 when FE is nonzero.

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