Q3 and q4 Q3 (4pts) Simple Circuits: What is the unknown RI? 1 (the same 04 (14p

Question

Q3 and q4

Q3 (4pts) Simple Circuits: What is the unknown RI? 1 (the same 04 (14pts)Two hollow conducting spheres of radius R1 and R2 are connected by a wire (see diagram). Before they were connected, sphere I had a charge of Q, and sphere 2 had an initial charge of 0. What is the charge on each sphere after they are connected by the wire? R1 0.2m; R2 0.1m; Q-9 micro coulombs ?a) (4pts) what are the charges Q1 and Q2 on each sphere ? b) (4pts) What is the electric potential V on each sphere? c) (4pts) What are the electric fields, El and E2, just above the surface of each sphere? d) (2pts) How does this example help explain why the Electric field is stronger near pointed surfaces than it is near flat surfaces on the same object?

Explanation / Answer

3)

by using kirchhoff's law for inner circuit,

E-I*R=0 ---(1)

by using kirchhoff's law for outer circuit,

E-I*R1+I*R=0 --(2)

from (1) and (2)

===> I*R-I*R1+I*R=0

2*I*R=I*R1

===> R1=2*R

4)

given ,

R1=0.2 m

R2=0.1 m

and

Q=9 uC =9*10^-6 C

let

the total charge on the sphere,

q1+q2=9*10^-6 C ----(1)

a)

after conneted by wire, the potential on the spheres,

V1=k*q1/R1

V2=k*q2/R2

and

V1=v2

k*q1/R1=k*q2/R2

===> q1/q2=R1/R2

q1/q2=0.2/0.1

==> q1/q2=2 -- --(2)

from (1) and (2)

q1=6 uC

q2=3 uC

b)

V1=k*q1/R1

v1=9*10^9*6*10^-6/(0.2)

V1=2.7*10^5 v

and

V2=k*q2/R2

v2=9*10^9*3*10^-6/(0.1)

v2=2.7*10^-6 v

c)

E1=k*q1/R1^2

=9*10^9*6*10^-6/(0.2)^2

=1.35*10^6 v/m

and

E2=k*q2/R2^2

=9*10^9*3*10^-6/(0.1)^2

=2.7*10^6 v/m

d)

here, R2< R1 ===> E2>E1

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