In the figure, an electron is shot at an initial speed of v 0 = 4 . 00 × 10 6 m s - 1 , at angle θ 0 = 40 . 0 ° from an x axis. It moves through a uniform electric field E → = ( 5 . 00 N C - 1 ) j ^ . A screen for detecting electrons is positioned parallel to the y axis, at distance x = 3 . 00 m . In unit-vector notation, what is the velocity of the electron when it hits the screen?

Due to the fact that the electron is negatively charged, then (as a consequence of equation and Newton's second law) the field E → pointing in the + y direction (which we will call "upward") leads to a downward acceleration. This is exactly like a projectile motion, where acceleration is given by a = e E / m = 8 . 78 × 10 11 m s 2 . Thus, equation gives t = x ν 0 c o s θ 0 = 3 . 00 m 4 . 00 × 10 6 m s - 1 cos 40 . 0 ° = 9 . 79 × 10 - 7 s . Now velocity in y - direction, (acceleration, a = e E m ) v y = v 0 sinθ 0 - a t = ( 4 . 00 × 10 6 m s - 1 ) sin 40 . 0 ° - 8 . 78 × 10 11 m s - 2 9 . 79 × 10 - 7 s = - 1 . 72 × 10 6 m s - 1 . Since the x component of velocity does not change, then the final velocity is v → = 3 . 06 × 10 6 m s - 1 i ^ - 1 . 72 × 10 6 m s - 1 j ^ .

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Find an expression for the oscillation frequency of an electric dipole of dipole moment $p$ and rotational inertia $I$ for small amplitudes of oscillation about its equilibrium position in a uniform electric field of magnitude $E$ .

Important Questions on Electric Fields

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IMPORTANT

Principles Of Physics International Student Version>Chapter 22 - Electric Fields>Problems>Q 44

At some instant, the velocity components of an electron moving between two charged parallel plates are

v_{x} = 2.5 \times 10^{5} m s^{- 1}

and

v_{y} = 5.0 \times 10^{3} m s^{- 1}

. Suppose, the electric field between the plates is uniform and given by

E = (126 N C^{- 1}) \hat{j} .

In unit-vector notation, what are (a) the electron's acceleration in that field and

(b)

the electron's velocity when its

x

-coordinate has changed by

2.0 cm ?

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Principles Of Physics International Student Version>Chapter 22 - Electric Fields>Problems>Q 45

A charged particle produces an electric field with a magnitude of

2.0 N C^{- 1}

at a point that is

50 cm

away from the particle. What is the magnitude of the field at an additional distance of

25 cm ?

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Principles Of Physics International Student Version>Chapter 22 - Electric Fields>Problems>Q 46

A certain electric dipole is placed in a uniform electric field $\vec{E}$ of magnitude $40 N C^{- 1}$ . Figure (given below) gives the magnitude $τ$ of the torque on the dipole versus the angle $θ$ between field $\vec{E}$ and the dipole moment $\vec{p}$ . The vertical axis scale is set by $τ_{s} = 80 \times 10^{- 28} N m$ . What is the magnitude of $\vec{P} ?$

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Principles Of Physics International Student Version>Chapter 22 - Electric Fields>Problems>Q 47

In the figure, a semi-infinite nonconducting rod (that is, infinite in one direction only) has uniform linear charge density $λ$ . $(a)$ Show that the electric field ${\vec{E}}_{n}$ at point $P$ makes an angle of $45 °$ with the rod and that this result is independent of the distance $R$ . ( Hint: Separately find the component of ${\vec{E}}_{p}$ parallel to the rod and the component perpendicular to the rod). $(b)$ Find the field magnitude for linear charge density $4.52 n {Cm}^{- 1}$ and $R = 3.80 cm$ .

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Principles Of Physics International Student Version>Chapter 22 - Electric Fields>Problems>Q 48

A disk of radius

2.5 cm

has a surface charge density of

7.0

μC m^{- 2}

on its upper face. What is the magnitude of the electric field produced by the disk at a point on its central axis at a distance of

z = 12 cm

from the disk?

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Principles Of Physics International Student Version>Chapter 22 - Electric Fields>Problems>Q 49

Figure shows two charged particles on the $x$ -axis: $- q =$ $- 3.20 \times 10^{- 19} C$ at $x = - 3.00 m$ and $q = 3.20 \times 10^{- 19} C$ at $x = + 3.00$ $m .$
What are the $(a)$ magnitude and (b) direction (relative to the positive direction of the $x$ axis) of the net electric field produced at the point $P$ at $y = 4.00 m ?$

$(c)$ What is the magnitude of the net field if $y$ is doubled?

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Principles Of Physics International Student Version>Chapter 22 - Electric Fields>Problems>Q 50

In the figure, an electron is shot at an initial speed of $v_{0} = 4.00 \times 10^{6}$ $m s^{- 1},$ at angle $θ_{0} = 40.0 °$ from an $x$
axis. It moves through a uniform electric field $\vec{E} = (5.00 N C^{- 1}) \hat{j} .$ A screen for detecting electrons is positioned parallel to the $y$ axis, at distance $x = 3.00 m .$ In unit-vector notation, what is the velocity of the electron when it hits the screen?

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Principles Of Physics International Student Version>Chapter 22 - Electric Fields>Problems>Q 51

The smaller of two concentric conducting shells has a uniform positive charge

q_{1}

. The larger shell has a uniform negative charge

- q_{2} .

Sketch the electric field lines between and outside the shells and give the direction of the external field lines as being either radially inward, radially outward, or nonexistent for these cases:

(a) q_{1} = q_{2}, (b) q_{1} > q_{2}

and

(c) q_{1} < q_{2}

Find an expression for the oscillation frequency of an electric dipole of dipole moment p and rotational inertia I for small amplitudes of oscillation about its equilibrium position in a uniform electric field of magnitude E.

Important Questions on Electric Fields

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Find an expression for the oscillation frequency of an electric dipole of dipole moment $p$ and rotational inertia $I$ for small amplitudes of oscillation about its equilibrium position in a uniform electric field of magnitude $E$ .