Question

The region of space between x=0 and x=3.0cm contains an increasing electric field E(x)=E0x/a in the...

The region of space between x=0 and x=3.0cm contains an increasing electric field E(x)=E0x/a in the positive x direction.If E0=5,0x10^3V/m and a=1.0cm.Find the potential diffrence between x=1.5cm and x=2.8cm.
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Answer #1

Ex = E0x/a

Ex = 5000a/0.01 = 500000 x

v = Edx

v = 5000 x^2/2

V = 5000* (0.028^2/2 -0.015^2/2)

V = -137.9 volts

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Answer #2

139.75 volt

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Answer #3

V = (integration)Edx

= (integration)(E0x/a)dx

= E0(x^2/2a)

so,

potential diffrence between x=1.5cm and x=2.8cm

= (E0/2a)*[(2.8*10^-2)^2 - (1.5*10^-2)^2]

= (5.0x10^3/0.02)*[(2.8*10^-2)^2 - (1.5*10^-2)^2]

= 139.75 volt

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Answer #4

V = (integration)Edx

= (integration)(E0x/a)dx

= E0(x^2/2a)

so,

potential diffrence between x=1.5cm and x=2.8cm

= (E0/2a)*[(1.5*10^-2)^2 - (2.8*10^-2)^2 ]

= (5.0x10^3/0.02)*[(1.5*10^-2)^2 - (2.8*10^-2)^2 ]

= -139.75 volt

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