Question

Two charged spheres placed 43 cm apart exert a force of 1.40 × 10-14 N

on each other. If one of the spheres has a charge of 1.68 × 10-17 C,

what is the charge of the other sphere?

Answer 1

Answer:

The force between two point charges obeys the Coulomb's law:

F = k\dfrac{|q_1||q_2|}{r^2}F=k  

r  

2

 

∣q  

1

​  

∣∣q  

2

​  

∣

​  

 

where q_1 = 1.68\times10^{-17}C,\space q_2q  

1

​  

=1.68×10  

−17

C, q  

2

​  

 are the charges of the first and second spheres respectively, r = 43cm = 0.43mr=43cm=0.43m is the distance between the spheres, and k = 9\times 10^9 N\cdot m^2/C^2k=9×10  

9

N⋅m  

2

/C  

2

 is the Coulomb's constant. Expressing the second charge and substituting F = 1.4\times 10^{-14}NF=1.4×10  

−14

N , obtain:

q_2 = \dfrac{Fr^2}{kq_1}\\ q_2 = \dfrac{1.4\times 10^{-14}\cdot 0.43^2}{9\times 10^9\cdot 1.68\times 10^{-17}} \approx 1.7\times 10^{-10}Cq  

2

​  

=  

kq  

1

​  

 

Fr  

2

 

​  

 

q  

2

​  

=  

9×10  

9

⋅1.68×10  

−17

 

1.4×10  

−14

⋅0.43  

2

 

​  

≈1.7×10  

−10

C

Answer. 1.7\times 10^{-10}C1.7×10  

−10

C.

Answer 2

Given:

Charge on one sphere is  $q_{1}$$=$ $1.68$×$10^{-17}$ C                            

The Force between the spheres $F$ $=$ $1.40$×$10^{-14}$

Distance between the spheres $r$ $=43$

To find:

The charge present on the other sphere.

Solution:

The force of attraction between two charged bodies as defined by Columb's Law is given by:

$F=\frac{q_{1} q_{2} }{4\pi r^{2} }$  where $q_{1}$ is the charge present one first body and $q_{2}$ is the charge present on another body and $r$ is the distance of separation between the bodies

Substitute these values in the formula of force and calculated the value of $q_{2}$ $F=\frac{q_{1} q_{2} }{4\pi r^{2} }$    

$1.40*10^{-14} =$ $\frac{1.68*10^{-17}q_{2} }{43^{2} }$

$\frac{1}{ q_{2}}$ $=$ $\frac{9*1.68}{1.4*43*43}*10^{9-7+14}$

$\frac{1}{ q_{2}}$ $=\frac{15.12}{2588.6}$ $*10^{16}$

${ q_{2}}=$ $1.71*10^{-18}$ C      

Thus, the charge on another sphere is $1.71*10^{-18}$ C