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In the diagram below, there are two charges of +q and -q and six points (a through f) at various distances from the two charges

In the diagram below, there are two charges of +q and -q and six points (a through f) at various distances from the two charges. Youwill be asked to rank changes in the electric potential along paths between pairs of points.

Using the diagram, rank each of the given paths on the basis of the change in electric potential. Rank the largest-magnitude positive change (increase in electricpotential) as largest and the largest-magnitude negative change (decrease in electric potential) as smallest.

Rank from largest to smallest. To rank items as equivalent, write them side by side.

a. from c to b

b. from c to d

c. from c to e

d. from d to a

e. from b to a

f. from f to e

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Answer #1

General guidance

Concepts and reason

This question is based on the concept of electric potential due to a charge particle and concept of potential difference.

First calculate electric potential at each marked point due to each charge particle using the general expression of electric potential and then find potential difference between them.

After that by comparing write them in decreasing order.

Fundamentals

Electric potential at any point is defined as the work required to be done to bring a unit charge from infinity to that point. Its unit is Volt and it is a scalar quantity.

The difference in potential of the two points is known as the potential difference. Its unit is also volt. If two-point A and B have potentials Va{V_a}and Vb{V_b} then potential difference from point A to B is calculated by the equation as follows:

Vab=Vb\u2212Va{V_{ab}} = {V_b} - {V_a}

HereVab{V_{ab}} is the potential difference between both points.

Electric potential at any point due to charge particle is calculated by the equation as follows;

V=kQrV = \\frac{{kQ}}{r}

HereVVis the potential at any point,kkis coulomb\u2019s constant,QQis charge on the particle andrris distance of the test point from the charge point.

Electric potential at any point due to combination of charges is calculate as follow:

Vnet=V1+V2+...Vn{V_{net}} = {V_1} + {V_2} + ...{V_n}

Here Vnet{V_{net}}is net potential at point due to various charge particle andV1{V_1} is the potential due to first charge, V2{V_2}is potential due to second charge and Vn{V_n} is potential due to nth charge.

Step-by-step

Step 1 of 2

Calculate net electric potential at point \u2018a\u2019 as follows;

Electric potential at point \u2018a\u2019 due to positive charge can be calculated as follows:

Substitute +q + qforQ1{Q_1}and 2x for the r1{r_1}in the equation V1=kQ1r1{V_1} = \\frac{{k{Q_1}}}{{{r_1}}} to calculate the potential at point \u2018a\u2019.

V1=kq2x{V_1} = \\frac{{kq}}{{2x}}

Electric potential at point \u2018a\u2019 due to negative charge can be calculated as follows:

Substitute \u2212q - qforQ2{Q_2}and 6x for the r2{r_2}in the equation V2=kQ2r2{V_2} = \\frac{{k{Q_2}}}{{{r_2}}} to calculate the potential at point \u2018a\u2019.

V2=\u2212kq6x{V_2} = - \\frac{{kq}}{{6x}}

Substitutekq2x\\frac{{kq}}{{2x}}forV1{V_1}and\u2212kq6x - \\frac{{kq}}{{6x}}forV2{V_2}in the equation Va=V1+V2{V_a} = {V_1} + {V_2}to determine the net potential at point a.

Va=kq2x\u2212kq6x=kq3x\\begin{array}{c}\\\\{V_a} = \\frac{{kq}}{{2x}} - \\frac{{kq}}{{6x}}\\\\\\\\ = \\frac{{kq}}{{3x}}\\\\\\end{array}

Therefore, net potential at point \u2018a\u2019 iskq3x\\frac{{kq}}{{3x}}.

Calculate net electric potential at point \u2018b\u2019.

Electric potential at point \u2018b\u2019 due to positive charge can be calculated as follows:

Substitute +q + qforQ1{Q_1}and xxfor the r1{r_1}in the equation V1=kQ1r1{V_1} = \\frac{{k{Q_1}}}{{{r_1}}} to calculate the potential at point \u2018b\u2019.

V1=kqx{V_1} = \\frac{{kq}}{x}

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