The drawing shows a parallel plate capacitor that is moving with a speed of v m/s through a magnetic field B. The velocity \overset{\rightarrow}{v} is perpendicular to the magnetic field. The electric field within the capacitor has a value of E N/C, and each plate has an area of A. What is the net force exerted on the positive plate of the capacitor?

Engineering

Physics

Parallel Plate Capacitor

Magnetic Field

Lorentz Force

Question

The drawing shows a parallel plate capacitor that is moving with a speed of v m/s through a magnetic field B. The velocity $\vec{v}$ is perpendicular to the magnetic field. The electric field within the capacitor has a value of E N/C, and each plate has an area of A. What is the net force exerted on the positive plate of the capacitor?

$ε_{0} AEvB$

$ε_{0} A \sqrt{\frac{E^{4}}{4} + E^{2} v^{2} B^{2}}$

$\frac{ε_{0} AEvB}{2}$

$\frac{ε_{0} {AE}^{2}}{2} + ε_{0} AEvB$

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${\vec{F}}_{E} = \frac{q^{2}}{2 ε_{0} A} (- \hat{i})$

${\vec{F}}_{B} = qvB (\hat{k})$

$E = \frac{q}{ε_{0} A}$