Question

Three point charges 1.0 µC, 0.10 µC and 10.0 µC are placed on a straight line
and net force on 0.10 µC is zero. Find x in cm.

Answer 1

Answer:

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Answer 2

The value of x is 9.48 cm

Step by step explanation

Although the image in the question is missing, you might be referring to the attached diagram.

Given:

Charge,q1 = 1.0 μC

Charge, q2 = 0.10 μC

Charge, q3 = 10.0 μC

Distance between q1 and q2 = 3 cm

Net force on q2, Fnet = 0 N

To find: x

Formula used

Let's use Coulombs equation to calculate force on q2 by q3 and q1.

Coulomb's equation :

F = k(q1q2)/ $r^{2}$

Here, F= electrostatic force

k = Coulomb's constant = 8.99 x $10^{9}$ N$m^{2}$$C^{-2}$

r = distance between charges

The force exerted on q2 by q1:

$F_{12}$ =  8.99 x $10^{9}$(1 x 0.10) / $3^{2}$

$F_{12}$ = 0.899 x $10^{9}$/ 9

$F_{12}$ = 9.98  x $10^{7}$C

Now, calculating the force exerted by q3 on q2:

$F_{32}$ = 8.99 x $10^{9}$( 0.10 x 10.0)/ $x^{2}$

$F_{32}$ = 8.99 x $10^{9}$/  $x^{2}$

Since the net force on charge q3 is zero:

$F_{12}$ = $F_{32}$

Equating both the equations, we get:

0.899 x $10^{9}$/ 9 = 8.99 x $10^{9}$/  $x^{2}$

$x^{2}$/ 9 = 10

$x^{2}$ = 90

$x^$ = 9.48 cm

Thus the value of x is 9.48 cm