Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

consider two concentric spherical shells, with radius R1=2.0 cm and R2 =4.0 cm,

ID: 1522649 • Letter: C

Question

consider two concentric spherical shells, with radius R1=2.0 cm and R2 =4.0 cm, uniformly charged, respectively, with surface charges Q1=+35.0 e-6 C and Q2= -25.0 e-6 C.

a) determine the electric field E(r) at a point distance r from the center ofthe shells for the cases: 1)r>R2 , 2)R1< r <R2, 3)r<R1 (NOTE you can express your results as a function of r)

b) what is the electric force F acting on a charge q= -2.0 nC located at r = 5.0cm away from the center of the shells? Indicated the direction of the force in a schematic diagram.

PLEASE GIVE ME DETAILED SOLUTIONS AND EXPLANATIONS THANK YOU

Explanation / Answer

a)


r > R2


consider a gaussian sphere of radius r

the charge inside the gaussian sphere = Q1+Q2


from gauss law

integration E*ds = qin/eo

E*4*pi*r^2 = (35-25)*10^-6/(8.84*10^-12)


E = 90019.76/r^2


++++++

b)


R1 < r < R2

consider a gaussian sphere of radius r

the charge inside the gaussian sphere = Q1


from gauss law

integration E*ds = qin/eo

E*4*pi*r^2 = 35*10^-6/(8.84*10^-12)


E = 315069.17/r^2


(c)


r < R1

consider a gaussian sphere of radius r

the charge inside the gaussian sphere = 0


from gauss law

integration E*ds = qin/eo

E*4*pi*r^2 = 0


E = 0


++++++++++++++++++++++


F = E*q =   (90019.76/0.05^2)*2*10^-9     = 0.072015808 N

the force towards the center of the sphere