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### University Physics with Modern Physics

Book edition 14th edition
Author(s) Hugh D. Young, Roger A. Freedman
Pages 1596 pages
ISBN 9780321973610

# In an electric trolley or bus system, the vehicle motor draws current from an overhead wire by means of a long arm with an attachment at the end that slides along the overhead wire. A brilliant electric spark is often seen when the attachment crosses a junction in the wires where contact is momentarily lost. Explain this phenomenon.

The insulation property of air breaks down due to presence of high back electromotive force (voltage) which induces when contactis momentarily lost, causing brilliant electric spark.

See the step by step solution

## Step 1: State Faraday’s law of induction and define insulation breakdown of air

Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced. Magnetic field can be varying by changing current with time which leads to time rate of magnetic flux .

$\epsilon =\frac{d{\varphi }_{B}}{dt}$

where $\epsilon \propto \frac{dI}{dt}$ is emf induced and $\frac{dI}{dt}$is time rate of current.

Insulation breakdown of material is the phenomenon when the insulating material fails to prevent flow of current through it under high voltage. The voltage at which breakdown of insulation property of material starts to happen, is called breakdown voltage. When the voltage applied across the material is greater than breakdown voltage, material become conducting, losing its insulation.

When the insulating material is air and voltage is higher than breakdown voltage of air then air loses its insulating property and converts into conducting material by ionizing itself called plasma which appears as electric spark.

## Step 2: Apply Faraday’s law of induction

The vehicle motor draws current from an overhead wire by means of a long arm with an attachment at the end that slides along the overhead wire. When this overhead wire momentarily loses contact with the long arm, current in the conducting arm reduces from larger value to zero in very short period of time. This leads to time rate of current having high value that is high rate of flux.

Now according to Faraday’s law, high rate of current or flux leads to induction of high back emf which is opposite to supply voltage. This back emf is so strong that it breaks the insulation property of air between overhead wire and vehicle arm, causing air to go through the insulation breakdown which leads to electric spark.

Thus, when contact is momentarily lost,the insulation property of air breaks down due to induction of high back electromotive force (voltage) causing brilliant electric spark.