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meriva
3 years ago
15

Particle A has charge qA and particle B has charge qB. When they are separated by a distance ri, they experience an attractive f

orce Fi. The particles are moved without altering their charges. Now they experience an attractive force with a magnitude of 16Fi. Find an expression for their new separation. (Use the following as necessary: qA, qB, ri, and ε0.)
Physics
1 answer:
kumpel [21]3 years ago
7 0

Answer:

r_{final}=r_{i}/4

Explanation:

We know force between 2 charges is given by

F=\frac{1}{4\pi \varepsilon }\frac{q_{1}q_{2}}{r^{2}}

It is given initial force is attractive of magnitudeF_{i}

Let r_{i} be the initial separation

Thus

F_{i}=\frac{1}{4\pi \varepsilon }\frac{q_{a}q_{b}}{r_{i}^{2}}

Now

Let r_{f} be the final separation

Thus final force becomes

\frac{1}{4\pi \varepsilon }\frac{q_{a}q_{b}}{r_{f}^{2}}

It is given F_{f} = 16F_{i}...................(i)

Using values of  F_{f} and F_{i} in equation i we have

16\times \frac{1}{4\pi \varepsilon }\frac{q_{a}q_{b}}{r_{i}^{2}} = \frac{1}{4\pi \varepsilon }\frac{q_{a}q_{b}}{r_{f}^{2}}

thus

thus\\\\(\frac{r_{i}}{r_{f}})^{2}=16\\\\\frac{r_{i}}{r_{f}}=4\\\\\therefore r_{f}=r_{i}/4

Thus the final separation is one-fourth of the initial separation

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