Question:

A conducting rod of length $l$ and mass $m$ is moving down a smooth inclined plane of inclination $\theta$ with constant velocity $v$. A current $i$ is flowing in the conductor in a direction perpendicular to paper inwards. A vertically upwards magnetic field $\vec{ B }$ exists in space. Then magnitude of magnetic field $\vec{ B }$ is

Updated On: Jun 23, 2023
  • $\frac{m g}{i l} \sin \theta$
  • $ \frac{mg}{il}\tan \theta $
  • $ \frac{mg\cos \theta }{il} $
  • $ \frac{mg}{il\,\sin \,\theta } $
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The Correct Option is B

Solution and Explanation

Magnetic force $\vec{ F }_{m}=i l B$ acts in the direction as shown in given figure. Rod will move downwards with constant velocity, if net force on it is zero.
or $ F_{m} \cos \theta=m g \sin \theta $ or $ i l B \cos \theta=m g \sin \theta $ $\therefore B=\left(\frac{m g}{i l}\right) \tan \theta$
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Current Electricity

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Alternating Current

The current electricity that is bidirectional and keeps changing the direction of the charge flow is known as alternating current. The bi-directionality is caused by a sinusoidally varying current and voltage that reverses directions, creating a periodic back-and-forth motion for the current. The electrical outlets at our homes and industries are supplied with alternating current.