Respuesta :
Answer:
a) [tex]F=1.04\times 10^{-5}\ N=1.04\ dyne[/tex]
b) [tex]F=1.05\times 10^{-5}\ N=1.05\ dyne[/tex]
Explanation:
Given:
- charge [tex]q_1=-12\times 10^{-9}\ C[/tex]
- charge [tex]q_2=-15\times 10^{-9}\ C[/tex]
- distance between the charges, [tex]d=0.395\ m[/tex]
a)
Now we know from the Coulombs law:
[tex]F=\frac{1}{4\pi.\epsilon_0} \times \frac{q_1.q_2}{d^2}[/tex]
[tex]F=9\times 10^9 \times \frac{12\times 10^{-9}\times 15\times 10^{-9}}{0.395^2}[/tex]
[tex]F=1.04\times 10^{-5}\ N=1.04\ dyne[/tex]
b)
On connecting the two charges via a conductor the two charges come to equilibrium.
[tex]F=9\times 10^9\times \frac{13.5\times 10^{-9}\times 13.5\times 10^{-9}}{0.395^2}[/tex]
[tex]F=1.05\times 10^{-5}\ N=1.05\ dyne[/tex]
Answer :
(a). The magnitude of the electric force exerted by one sphere on the other is [tex]10.38\times10^{-6}\ N[/tex]
(b). The electric force each exerts on the other after they have come to equilibrium is [tex]1.05\times10^{-5}\ N[/tex]
Explanation:
Given that,
Distance = 0.395 m
Charge of first sphere = -12.0 nC
Charge of second sphere = -15.0 nC
(a). We need to calculate the magnitude of the electric force exerted by one sphere on the other
Using formula of electric force
[tex]F=\dfrac{kq_{1}q_{2}}{r^2}[/tex]
Where, [tex]q_{1}=-12.0\ nC[/tex]
[tex]q_{2}=-15.0\ nC[/tex]
r = distance
Put the value into the formula
[tex]F=\dfrac{9\times10^{9}\times12.0\times10^{-9}\times15\times10^{-9}}{(0.395)^2}[/tex]
[tex]F=10.38\times10^{-6}\ N[/tex]
(b). The identical spheres are connected by a conducting wire.
Both charges are same so the force is repulsive.
We need to calculate the net charge
Using formula of charge
[tex]Q=\dfrac{q_{1}+q_{2}}{2}[/tex]
Put the value into the formula
[tex]Q=\dfrac{(-12.0-15.0)\times10^{-9}}{2}[/tex]
[tex]Q=-13.5\times10^{-9}\ C[/tex]
We need to calculate the magnitude of the electric force each exerts on the other after they have come to equilibrium
Using formula of electric force
[tex]F=\dfrac{kQ^2}{r^2}[/tex]
Put the value into the formula
[tex]F=\dfrac{9\times10^{9}\times(-13.5\times10^{-9})^2}{(0.395)^2}[/tex]
[tex]F=1.05\times10^{-5}\ N[/tex]
Hence, (a). The magnitude of the electric force exerted by one sphere on the other is [tex]10.38\times10^{-6}\ N[/tex]
(b). The electric force each exerts on the other after they have come to equilibrium is [tex]1.05\times10^{-5}\ N[/tex]
