What is the relationship between velocity and induced EMF as defined in the formula E = B l v?

• A. Directly proportional
• B. Inversely proportional
• C. Unrelated
• D. Dependent on resistance

Answer: (A)

The relationship between velocity and induced electromotive force (EMF) as defined in the formula (E = B l v) is directly proportional. This equation indicates that the induced EMF (E) is a product of the magnetic flux density (B), the length of the conductor (l), and the velocity (v) of the conductor moving through the magnetic field.

When the velocity increases, assuming that both the magnetic flux density and the length of the conductor remain constant, the induced EMF will also increase proportionally. This means that if you double the velocity of the conductor, the induced EMF will also double, demonstrating a direct relationship between these two quantities.

In the context of the other options, while inversely proportional would suggest that an increase in velocity would lead to a decrease in induced EMF, that does not align with the formula. The concept of being unrelated does not apply either, as there is a clear mathematical relationship established. Finally, stating that the relationship is dependent on resistance does not capture the essence of this particular formula; resistance may influence current flow but does not directly impact the relationship between induced EMF and velocity in the context of this equation.