Falling charges, how many will succeed?

Electricity and Magnetism Level 5

A horizontal conducting cylindrical hollow pipe of radius R = 54 mm R = 54\text{ mm} and length L = 100 cm ( R < < L ) L = 100 \text{ cm} (R<<L) has a small hole P P at its top, at the middle of the length as shown in the figure. Drops of mass M = 231 mg M = 231 \text{ mg} and charge q = 1 nC q = 1 \text{ nC} are falling into the hole from point A A , at height 2 R 2R measured from the axis of the cylinder. Assume that the charge in the fallen drop gets uniformly distributed over the surface of the cylinder and charge distributed on cylinder remains uniform throughout. If the number of drops that will be able to enter the cylinder is given as n = x × 1 0 y n = x \times10^y in scientific notation. Find the value of x + y x + y .


The answer is 5.

Nishant Rai by Nishant Rai , 25, India

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2 solutions

Aniket Sanghi
Sep 29, 2016

Good question !

The exact answer is 9.79 × 1 0 3 9.79 × 10^3

0 Helpful 0 Interesting 0 Brilliant 0 Confused

i got 9800 exact!

Prakhar Bindal - 4 years, 8 months ago

what's so "good" in it ??

A Former Brilliant Member - 4 years, 4 months ago
Nishant Rai
Jun 10, 2015

0 Helpful 0 Interesting 0 Brilliant 2 Confused

Exact result for n n isn't 1 0 4 10^4 , even if we say it is 1 0 4 10^4 , there are infinitely many pairs ( x , y ) (x,y) that satisfy equation x 1 0 y = 1 0 4 x 10^y=10^4 . So you should change answer form.

Miloje Đukanović - 5 years, 9 months ago

Exact answer is 9.79 × 1 0 3 9.79 × 10^3

Btw good q :)

Aniket Sanghi - 4 years, 8 months ago

What does λ \lambda represent here?

Joe Mansley - 1 year, 5 months ago

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