Show Question Details t has a charge of +12.1 nC is at the origin. (a) What is (

Question

Show Question Details t has a charge of +12.1 nC is at the origin. (a) What is (are) the shape(s) of the equipotential surfaces in the region around this charge? This answer has not been graded yet. (b) Assuming the potential to be zero atr-co, calculate the radii of the five surfaces that have potentials equal to 18.0 V, 36.0 V, 54.0 V, 72.0 V, and 90.0 V, and sketch them to scale centered on the charge.(Give your answer to at least two decimal places.) V (V) 18.0 36-054.0 72.0 90.0 Choose File no file selected This answer has not been graded yet. (c) Are these surfaces equally spaced? Explain your answer This answer has not been graded yet. (d) Estimate the electric field strength between the 36.0-V and 54.0-V equipotential surfaces by dividing the difference between the two potentials by the difference between the two radii. Eest V/m Compare this estimate to the exact value at the location midway between these two surfaces.

Explanation / Answer

Given

a)

charge of q = 12.1 nC at origin

we know that the equipotential surfaces , for the point charge in plane these are of concentric circles with different radius and

the equipotential surface is the region along which we can measure the potential difference is always zero

v = k*q/r

b) Given potential are 18.0 V , 36.0 V ,72.0 V ,90V

we know the potential ata point r from a charge q is v = k*q/r

so 18 = 9*10^9*12.1*10^-9/r ===> r = 6.05 m from the center

for V = 36 V

v = k*q/r

so 36 = 9*10^9*12.1*10^-9/r ===> r = 3.025 m from the center

for V = 54 V

v = k*q/r

so 54 = 9*10^9*12.1*10^-9/r ===> r = 2.01 m from the center

for V = 72 V

v = k*q/r

so 72 = 9*10^9*12.1*10^-9/r ===> r = 1.5125 m from the center

for V = 90 V

v = k*q/r

so 90 = 9*10^9*12.1*10^-9/r ===> r = 1.21 m from the center

c)

no these surfaces are not equally spaced .

d) for 36 v the radius is r1 = 3.025 m for 54 V the radius is r2 =2.01 m

from the relation V = E*d

E = V/d

E = (v2-v1)/(d)

E = (54-36)/(3.025-2.01) V/m

E = 17.734 V/m

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