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Chapter 25: Q.37 (page 711)

Two point charges 2.0 cm apart have an electric potential energy -180 mJ. The total charge is 30 nC. What are the two charges?

Short Answer

Expert verified

The charges value of two points are 40nC and -10nC

Step by step solution

01

Step 1: Definition the equation of the potential energy of a point

For the Two charge points

$U = 1 / (4 π ε_{0}) \frac{q_{1} q_{2}}{r} U = - 180 μ J r = 2 c m ε_{0} = 8.85 \times 10^{- 12} C^{2} / N \times m^{2} U = 1 / (4 π ε_{0}) \frac{q_{1} q_{2}}{r} - 180 μ J = 1 / (4 π ε_{0}) \frac{q_{1} q_{2}}{r} q_{1} q_{2} = (- 180 μ J) (8.85 \times 10^{- 12} C^{2} / N \times m^{2}) (2 c m) = - 4 \times 10^{- 16} C^{2}$

As per the basis of the question

localid="1648127293201" $q_{1} = 30 \times 10^{- 9} C - q_{2}$

Now, applying given value of $q_{2}$ in above equation

$q_{2} = - 1 \times 10^{- 8} C = - 10 n C$

02

Definition the equation of the potential energy of two points

Applying the value of $q_{2} i n q_{1} e q u a t i o n$

$q_{1} = 40 n C$

The charges values of two points are 40 nC and -10 nC

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Most popular questions from this chapter

What potential difference is needed to accelerate a $He +$ ion (charge $+ e, mass 4 u$ ) from rest to a speed of $2.0 \times 10^{6} m / s$ ?

A proton is fired from far away toward the nucleus of an iron atom. Iron is element number $26$ , and the diameter of the nucleus is $9.0 f m$ . What initial speed does the proton need to just reach the surface of the nucleus? Assume the nucleus remains at rest.

FIGURE Q25.6 shows the electric potential along the x-axis.

a. Draw a graph of the potential energy of a $0.1 C$ charged particle. Provide a numerical scale for both axes.

b. If the charged particle is shot toward the right from FIGURE Q25.6 $x = 1 m$ with $1.0 J$ of kinetic energy, where is its turning point? Use your graph to explain.

a. Find an algebraic expression for the electric field strength $E_{0}$ at the surface of a charged sphere in terms of the sphere’s potential $V_{0}$ and radius $R$ .

b. What is the electric field strength at the surface of a $1.0 - c m$ -diameter marble charged to $500 V$ ?

An electron moves along the trajectory of $F I G U R E Q 25.3$ from $i$ to $f$ .
$(a)$ Does the electric potential energy increase, decrease, or stay the same? Explain.
$(b)$ Is the electron's speed at $f$ greater than, less than, or equal to its speed at $i$ ? Explain.

See all solutions

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