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Indian Institute of Technology Kharagpur

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Problem 55

Designing a sparker Your friend decides to use a device that converts some mechanical energy into the production of a spark to ignite lighter fluid. Use the information and the questions below to decide whether his sparker will work. The sparker has a coil connected across a very short gap $(0.1 \mathrm{mm})$ between the ends of the wire in the coil. (a) Estimate the potential difference needed across this gap to cause dielectric breakdown (a spark) to ignite the fumes from the

wick. Dielectric breakdown occurs when the magnitude of the E field is 3 * 106 V/m or greater. (b) Estimate, based on mechanical properties, the shortest time interval that you think a person can push a small magnet from several centimeters away to the surface of a coil. (c) As the magnet is pushed

toward the coil, the field in the coil increases and causes an induced emf. If the magnetic flux inside one loop increases by 10-6 T # m2 as the magnet moves forward, how many coil turns are needed to produce the emf to cause a spark? Is this a reasonable lighter system?

Answer

a) 300 $\mathrm{V}$

b) 0.010 $\mathrm{s}$

c) $3 \times 10^{6}$ turns

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## Discussion

## Video Transcript

in this particle. Their problem. The electric failure is given by three time stand to the six. What per meter? The gap distances given as 0.1 millimeter. So that is 10 to the negative. Four meter from here. Bought a The potential defense native is given by E Much. Died by D so that comes out to be three times 10 to the six time stand to the negative. Four volt equals three times 10 to the two fold equals 300. Vote Barbie estimates based on mechanical properties. Where is the shortest time interval that you think you can push or pull a magnet? Mm, You can, depending on your reflects action. Human reflex action! Ease about 100 off a second. So I will put that number down. This is that number. This is the human reflex action dying. So you will need at this little Prince Ito one second or 100 off a second to move the magnet part C as the manatees push towards the corn in the fields in the card increases and causing MF the fox is given So flocks is given as 10 to the negative six Just the meter square. How many turn do you need? Okay, so the changing flux is this So use need to provide. We know that induced electric field is given by number of stars and then the change in stocks over the change in time. In this particular case, we're looking for the number of times it is advisable to right this as the desert notation Delta fee over Delta T and this is my delta t over here. And the change in flux is startled. A fee. So end goes as yeah. Does Ducky over Delta Fee So that number will come out to be three times 10 to the No, that's 300. I'm sorry. This is 300 voltage for E. Delta is 0.1 2nd divided by the fees tend to the negative six. So that comes out to be over here. I have got three and these cunts, the denominator and becomes tend to the six. So basically, you will need three 1,000,000 charms and getting a three million turn. It's really hard. So you can safely say that this is unfeasible. However, however, what you can do is you can use three step up transformers, both of them are will step it by 100 times. One step up transformer and the second step up transformer, which will get you up by 100 times and 1/3 step up transformer. Let's say it will get it, get you up by 300 times. If you use three step up transformers in cities, then you will be able to actually read, but just $3 billion. It is virtually the unfeasible.

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Magnetic field values are often determined by using a device known as a search coil. This technique depends onthe measurement of the total charge passing through a coil in a time interval during which the magnetic flux linking the windings changes either because of the coil’s motion or because of a change in the value of B. (a) Show that as the flux through the coil changes from $\Phi_{1}$ to $\Phi_{2},$ the charge transferred through the coil is given by $Q=N\left(\Phi_{2}-\Phi_{1}\right) / R,$ where $R$ is the resistance of the coil and $N$ is the number of turns. (b) As a specific example, calculate $B$ when a total charge of $5.00 \times 10^{-4} \mathrm{C}$ passes through a 100 -turn coil of resistance 200$\Omega$ and cross-sectional area 40.0 $\mathrm{cm}^{2}$ as it is rotated in a uniform field from a position where the plane of the coil is perpendicular to the field to a position where it is parallel to the field.