A very long insulating cylinder of charge of radius 2.60 cm carries a uniform linear density of 15.0 nC/m . Part A If you put one probe of a voltmeter at the surface, how far from the surface must the other probe be placed so that the voltmeter reads 200 V

Given Information:  

Radius = ra = 2.60 cm = 0.026 m

Density = J = 15.0 nC/m

change in potential difference = ΔV = 200 V

Required Information:  

Distance = d = ?

distance = 0.088 m

Explanation:

As we know

ΔV = Vb - Va = J/4πε₀*ln(rb/ra)

Where ra and rb is the point where potential difference is Va and Vb respectively

1/4πε₀ = 9x10⁹ N.m²/C²

We want to find the distance d = rb - ra

ΔV = J/4πε₀*ln(rb/ra)

200 = 9x10⁹*15x10⁻⁹*ln(rb/ra)

200/135 = ln(rb/ra)

1.48 = ln(rb/ra)

taking e on both sides yields

e^(1.48) = rb/ra

4.39 = rb/ra

rb = 4.39*0.026

rb = 0.114 m

Therefore, the required distance is

d = rb - ra

d = 0.114 - 0.026

d = 0.088 m

Therefore, the other probe must be placed 0.088 m from the surface so that the voltmeter reads 200 V

the first american roller coaster was the mauch chunk switchback railway, built in the mountains of pennsylvania in the mid-1800s. the track, originally built to send coal to a railway, was reconfigured as a "scenic tour."

  the grams     of oxygen gas   that can be produced     is 20.6   grams of o₂

calculation

2liclo₃ →   2 licl + 3 o₂

step 1:   find the moles of liclo₃

moles = mass÷ molar mass

from periodic table the molar mass of liclo₃ =6.9 +35.5   +(16 x3) =90.4 g/mol

moles=38.7 g÷90.4 g/mol=0.4281   moles

step 2:   use the   mole ratio   to calculate the moles of o2

from equation above, liclo₃: o₂   is 2: 3  

therefore the moles of   o₂=0.4281 moles x3/2 =0.6422   moles

step 3: find mass   of o₂

mass= moles x molar mass

from periodic table the   molar mass of   o₂ = 16 x2= 32 g/mol

mass=0.6422   moles   x   32 g/mol = 20.6 grams of o₂