Question

In the figure below, how much work is required to bring the charge
Q = +16e
and initially at rest, along the dashed line from infinity to the indicated point near two fixed particles of charges
q1 = +4e
and
q2 = −q1/2?
Distance
d = 1.40 cm,
θ1 = 41°,
and
θ2 = 58°.

Answer 1

Answer on Question #65280-Physics-Other

In the figure below, how much work is required to bring the charge $Q = +16e$ and initially at rest, along the dashed line from infinity to the indicated point near two fixed particles of charges $q1 = +4e$ and $q2 = -q1/2$ ?

Distance $d = 1.40 \, \text{cm}$ , $\theta 1 = 41{}^\circ$ , and $\theta 2 = 58{}^\circ$ .

Solution

$V(\infty) = 0$

The potential from point charge $q$ is

$V = \frac{kq}{r}$

The initial potential:

$V_{in} = V(\infty) = 0$

The final potential:

$V_{fin} = k\left(\frac{q_1}{2d} + \frac{q_2}{d}\right) = k\left(\frac{q_1}{2d} - \frac{q_1}{2d}\right) = 0.$

The potential difference is

$V_{fin} - V_{in} = 0 - 0 = 0.$

The total work is

$W = Q\big(V_{fin} - V_{in}\big) = 0$

Answer: 0 J.

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