Exam 16: Electric Charge and Electric Field

Two point charges $q = - 8.50 \mu \mathrm { C }$ are fixed $10.0 \mathrm {~cm}$ apart along a horizontal bar, as shown in the figure. Their electrical forces will be used to balance the weight of a very small sphere carrying a charge $Q = + 15.0 \mu \mathrm { C } , 10.0 \mathrm {~cm}$ from each of them in a place where $g = 9.80 \mathrm {~m} / \mathrm { s } 2$ . What is the greatest mass $M$ this sphere can have without falling? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \right.$ $\left. \mathrm { N } \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Two tiny particles having charges $+ 20.0 \mu \mathrm { C }$ and $- 8.00 \mu \mathrm { C }$ are separated by a distance of $20.0 \mathrm {~cm}$ . What are the magnitude and direction of electric field midway between these two charges? $( k = 1 / 4$ $\pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

Four point charges $Q$ of equal magnitude and sign are arranged on three of the corners of the square of side $d$ as shown in the figure Which one of the arrows shown represents the net force acting on the charge at the upper right hand corner of the square?

Two tiny beads, each of mass $3.2 \mathrm {~g}$ , carry equal-magnitude charges. When they are placed $6.4 \mathrm {~cm}$ apart and released in outer space, they begin to accelerate toward each other at $538 \mathrm {~m} / \mathrm { s } ^ { 2 }$ . What is the magnitude of the charge on each bead? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right.$ )

Two point charges, $Q _ { 1 }$ and $Q _ { 2 }$ , are separated by a distance $R$ . If the magnitudes of both charges are halved and their separation is also halved, what happens to the electrical force that each charge exerts on the other one?

The figure shows electric field lines arising from two small charged particles $P$ and $Q$ . Consider the following two statements: (i) The charge on $\mathrm { P }$ is smaller than the charge on $\mathrm { Q }$ . (ii) The electrostatic force on $\mathrm { P }$ is smaller than the force on $Q$ . Which of the above statements are true?

As shown in the figure, three small charges are equally spaced on the arc of a circle that is centered at the charge $Q$ , where $Q = + 23 \mathrm { nC }$ and all the other quantities are accurate to two significant figures. What is the magnitude of the net electric force on the charge $Q$ due to the other three charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

An electron is initially moving to the right when it enters a uniform electric field directed upwards, as shown in the figure. Which trajectory $( \mathbf { X } , \mathbf { Y } , \mathbf { Z }$ , or $\mathbf { W } )$ will the electron follow in the field?

Three point charges are placed on the $x$ -axis, as follows. A charge of $+ 2.0 \mu \mathrm { C }$ is at the origin, a charge of $- 2.0 \mu \mathrm { C }$ is at $x = 50 \mathrm {~cm}$ , and a charge of $+ 4.0 \mu \mathrm { C }$ is at $x = 100 \mathrm {~cm}$ . What are the magnitude and direction of the electrostatic force on the charge at the origin due to the other two charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Four tiny charged particles (two having a charge $+ Q$ and two having a charge $- Q$ ) are distributed on the $x$ - and $y$ -axes as shown in the figure. Each charge is equidistant from the origin. In which direction is the net electric field at the point $P$ on the $y$ -axis?

$\mathrm { A } + 5.00 - \mu \mathrm { C }$ point charge is placed at the $0.0 \mathrm {~cm}$ mark of a meter stick and a $- 4.00 - \mu \mathrm { C }$ point charge is placed at the $50.0 \mathrm {~cm}$ mark. At what point on a line through the ends of the meter stick is the electric field equal to zero?

An electron is placed in a uniform electric field of $4.5 \times 104 \mathrm {~N} / \mathrm { C }$ that points to the right. $( e =$ $1.6 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {electron } } = 9.11 \times 10 - 31 \mathrm {~kg}$ ) (a) What are the magnitude and direction of the force on the electron? (b) If the electron is released from rest, what is its speed after $3.0 \mathrm { ps }$ ?

Four point charges of equal magnitude but with varying signs are arranged on three of the corners and at the center of the square of side $d$ as shown in the figure. Which one of the arrows shown represents the net force acting on the center charge?

A pair of charged conducting plates produces a uniform field of $12,000 \mathrm {~N} / \mathrm { C }$ , directed to the right, between the plates. The separation of the plates is $40 \mathrm {~mm}$ . An electron is projected from plate $A$ , directly toward plate $\mathrm { B }$ , with an initial speed of $v _ { 0 } = 2.0 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$ . What is the speed of the electron as it strikes plate $B$ ? $\left( e = 1.6 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} \right)$

$\mathrm { A } + 5.0 - \mu \mathrm { C }$ point charge is placed at the $0 \mathrm {~cm}$ mark of a meter stick and a $- 4.0 - \mu \mathrm { C }$ charge is placed at the $50 \mathrm {~cm}$ mark. What is the net electric field at the $30 \mathrm {~cm}$ mark? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \right.$ . $m ^ { 2 } / C ^ { 2 }$ )

An asteroid of mass $58,000 \mathrm {~kg}$ carrying a negative charge of $15 \mu \mathrm { C }$ is $180 \mathrm {~m}$ from a second asteroid of mass $52,000 \mathrm {~kg}$ carrying a negative charge of $11 \mu \mathrm { C }$ . What is the magnitude of the net force the asteroids exert upon each other, assuming we can treat them as point particles? $\left( G = 6.67 \times 10 ^ { - 11 } \right.$ $\mathrm { N } \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } , k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A proton is located at the point $( x = 1.0 \mathrm {~nm} , y = 0.0 \mathrm {~nm} )$ and an electron is located at the point $( x = 0.0 \mathrm {~nm} , y = 4.0 \mathrm {~nm} )$ . Find the magnitude of the electrostatic force that each one exerts on the other. $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , e = 1.6 \times 10 ^ { - 19 } \mathrm { C } \right)$

Three identical $3.0 - \mu \mathrm { C }$ charges are placed at the vertices of an equilateral triangle that measures 30 $\mathrm { cm }$ on a side. What is the magnitude of the electrostatic force on any one of the charges? $( k = 1 / 4 \pi$ $\varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

What is the magnitude of a the vertical electric field that will balance the weight of a plastic sphere of mass $2.1 \mathrm {~g}$ that has been charged to $- 3.0 \mathrm { nC }$ ? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A thin spherical metal shell of radius $8.0 \mathrm {~cm}$ carries $7.5 \mu \mathrm { C }$ of excess charge. What is the magnitude of the electric field it produces at the following places? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \right.$ $\mathrm { N } \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ ) (a) at $1.0 \mathrm {~cm}$ above the surface (b) at $7.0 \mathrm {~cm}$ from the center of the sphere