Deck 23: The Electric Field

Question 1

Three equal negative point charges are placed at three of the corners of a square of side d.What is the magnitude of the net electric field at the center of the square? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

Answer 1

E = 2kq/d²

Question 2

The figure shows two unequal point charges,q and Q,of opposite sign.Charge Q has greater magnitude than charge q.In which of the regions X,Y,Z will there be a point at which the net electric field due to these two charges is zero?

A) only regions X and Z
B) only region X
C) only region Y
D) only region Z
E) all three regions

Answer 2

only region X

Question 3

A metal sphere of radius 10 cm carries a charge of +2.0 μC uniformly distributed over its surface. What is the magnitude of the electric field due to this sphere at a point 5.0 cm outside the sphere's surface? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

A) 4.0 × 10⁵ N/C
B) 8.0 × 10⁵ N/C
C) 4.2 × 10⁶ N/C
D) 4.0 × 10⁷ N/C
E) 8.0 × 10⁷ N/C

Answer 3

8.0 × 10⁵ N/C

Question 4

Two point charges,Q₁ = -1.0 μC and Q₂ = + 4.0 μC,are placed as shown in the figure.
(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)The y component of the electric field,at the origin O,is closest to

A) 6.0 × 10^-3 N/C.
B) -6.0 × 10^-3 N/C.
C) 3.8 × 10^-3 N/C.
D) -3.8 × 10^-3 N/C.
E) 7.1 × 10^-3 N/C.

Question 5

An electron is initially moving to the right when it enters a uniform electric field directed upwards.Which trajectory shown below will the electron follow?

A) trajectory W
B) trajectory X
C) trajectory Y
D) trajectory Z

Question 6

Two point charges of +20.0 μC and -8.00 μC are separated by a distance of 20.0 cm.What is the magnitude of electric field due to these charges at a point midway between them?
(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

A) 25.2 × 10⁶ N/C directed toward the negative charge
B) 25.2 × 10⁶ N/C directed toward the positive charge
C) 25.2 × 10⁵ N/C directed toward the negative charge
D) 25.2 × 10⁵ N/C directed toward the positive charge
E) 25.2 × 10⁴ N/C directed toward the negative charge

Question 7

The figure shows three electric charges labeled Q₁,Q₂,Q₃,and some electric field lines in the region surrounding the charges.What are the signs of the three charges?

A) Q₁ is positive, Q₂ is negative, Q₃ is positive.
B) Q₁ is negative, Q₂ is positive, Q₃ is negative.
C) Q₁ is positive, Q₂ is positive, Q₃ is negative.
D) All three charges are negative.
E) All three charges are positive.

Question 8

What is the minimum magnitude of an electric field that balances the weight of a plastic sphere of mass 6.4 g that has been charged to -3.0 nC?

A) 2.1 × 10⁷ N/C
B) 2.4 × 10⁶ N/C
C) 4.5 × 10⁶ N/C
D) 6.4 × 10⁶ N/C

Question 9

A point charge Q of mass 8.50 g hangs from the horizontal ceiling by a light 25.0-cm thread.When a horizontal electric field of magnitude 1750 N/C is turned on,the charge hangs away from the vertical as shown in the figure.The magnitude of Q is closest to

A) 27.5 µC.
B) 47.6 µC.
C) 55.0 µC.
D) 3.0 µC.
E) 3.5 µC.

Question 10

A proton is placed in an electric field of intensity 700 N/C.What are the magnitude and direction of the acceleration of this proton due to this field? (m_proton = 1.67 × 10^-27 kg,e = 1.60 × 10^-19C)

A) 6.71 × 10⁹ m/s² opposite to the electric field
B) 6.71 × 10¹⁰ m/s² opposite to the electric field
C) 6.71 × 10¹⁰ m/s² in the direction of the electric field
D) 67.1 × 10¹⁰ m/s² opposite to the electric field
) 67.1 × 10¹⁰ m/s² in the direction of the electric field

Question 11

Three +3.0-μC point charges are at the three corners of a square of side 0.50 m. The last corner is occupied by a -3.0-μC charge. Find the magnitude of the electric field at the center of the square.
(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

Question 12

The electric field 1.5 cm from a very small charged object points toward the object with a magnitude of 180,000 N/C.What is the charge on the object? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

A) -4.5 nC
B) +4.5 nC
C) -5.0 nC
D) +5.0 nC

Question 13

A small sphere with a mass of 441 g is moving upward along the vertical +y-axis when it encounters an electric field of 5.00 N/C . If,due to this field,the sphere suddenly acquires a horizontal acceleration of 13.0 m/s²


,what is the charge that it carries?

A) 1.15 C
B) -1.15 C
C) 1150 C
D) -1150 C

Question 14

Two point charges Q₁ and Q₂ of equal magnitudes and opposite signs are positioned as shown in the figure.Which of the arrows best represents the net electric field at point P due to these two charges?

A) A
B) B
C) C
D) D
E) The field is equal to zero at point P.

Question 15

Three equal negative point charges are placed at three of the corners of a square of side d as shown in the figure.Which of the arrows represents the direction of the net electric field at the center of the square?

A) A
B) B
C) C
D) D
E) The field is equal to zero at point P.

Question 16

An atomic nucleus has a charge of +40e. What is the magnitude of the electric field at a distance of
1)0 m from the center of the nucleus? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²,e = 1.60 × 10^-19C)

A) 5.4 × 10^-8 N/C
B) 5.6 × 10^-8 N/C
C) 5.8 × 10^-8 N/C
D) 6.0 × 10^-8 N/C
E) 6.2 × 10^-8 N/C

Question 17

A small glass bead has been charged to 8.0 nC.What is the magnitude of the electric field 2.0 cm from the center of the bead? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

A) 1.8 × 10⁵ N/C
B) 3.6 × 10³ N/C
C) 1.4 × 10^-3 N/C
D) 3.6 × 10^-6 N/C

Question 18

A point charge Q = -500 nC and two unknown point charges,q₁ and q₂,are placed as shown in the figure.The electric field at the origin O,due to charges Q,q₁ and q₂,is equal to zero.The charge q₁ is closest to

A) 130 nC.
B) 76 nC.
C) 150 nC.
D) -76 nC.
E) -130 nC.

Question 19

A 5.0-μC point charge is placed at the 0.00 cm mark of a meter stick and a -4.0-μC point charge is placed at the 50 cm mark. At what point on a line joining the two charges is the electric field due to these charges equal to zero?

Question 20

Four equal negative point charges are located at the corners of a square,their positions in the xy-plane being (1,1),(-1,1),(-1,-1),(1,-1).The electric field on the x-axis at (1,0)points in the same direction as

A)
B)
C) -
D)
E) -

Question 21

At a distance of 4.3 cm from the center of a very long uniformly charged wire,the electric field has magnitude 2000 N/C and is directed toward the wire.What is the charge on a 1.0 cm length of wire near the center? (ε₀ = 8.85 × 10^-12 C²/N • m²)

A) -0.048 nC
B) -0.052 nC
C) -0.044 nC
D) -0.056 nC

Question 22

An electric dipole is made of two charges of equal magnitudes and opposite signs.The positive charge,q = 1.0 μC,is located at the point (x,y,z)= (0.00 cm,1.0 cm,0.00 cm),while the negative charge is located at the point (x,y,z)= (0.00 cm,-1.0 cm,0.00 cm).How much work will be done by an electric field = (3.0 × 10⁶ N/C)
To bring the dipole to its stable equilibrium position?

A) 0.060 J
B) 0.030 J
C) 0.00 J
D) 0.020 J
E) 0.12 J

Question 23

A pair of charged conducting plates produces a uniform field of 12,000 N/C,directed to the right,between the plates.The separation of the plates is 40 mm.An electron is projected from plate A,directly toward plate B,with an initial velocity of v_o = 2.0 × 10⁷ m/s,as shown in the figure.(e = 1.60 × 10^-19 C,
Ε₀ = 8.85 × 10^-12 C²/N • m²,m_el = 9.11 × 10^-31 kg)The velocity of the electron as it strikes plate B is closest to

A) 1.2 × 10⁷ m/s.
B) 1.5 × 10⁷ m/s.
C) 1.8 × 10⁷ m/s.
D) 2.1 × 10⁷ m/s.
E) 2.4 × 10⁷ m/s.

Question 24

An initially-stationary electric dipole of dipole moment = (5.00 × 10^-10 C • m)
Placed in an electric field
= (2.00 × 10⁶ N/C)
+ (2.00 × 10⁶ N/C)
)What is the magnitude of the maximum torque that the electric field exerts on the dipole?

A) 2.00 × 10^-3 N • m
B) 1.40 × 10^-3 N • m
C) 2.80 × 10^-3 N • m
D) 0.00 N • m
E) 1.00 × 10^-3 N • m

Question 25

In the figure,a ring 0.71 m in radius carries a charge of + 580 nC uniformly distributed over it.A point charge Q is placed at the center of the ring.The electric field is equal to zero at field point P,which is on the axis of the ring,and 0.73 m from its center.(ε₀ = 8.85 × 10^-12 C²/N • m²)The point charge Q is closest to

A) -210
B) -300
C) -420
D) 210
E) 300

Question 26

Two thin 80.0-cm rods are oriented at right angles to each other.Each rod has one end at the origin of the coordinates,and one of them extends along the +x-axis while the other extends along the +y-axis.The rod along the +x-axis carries a charge of -15.0 µC distributed uniformly along its length,and the other rod carries +15.0 µC uniformly over its length.Find the magnitude and direction of the net electrical force that these two rods exert on an electron located at the point (40.0 cm,40.0 cm).(e = 1.60 × 10^-19 C,
ε₀ = 8.85 × 10^-12 C²/N • m²)

Question 27

A pair of charged conducting plates produces a uniform field of 12,000 N/C,directed to the right,between the plates.The separation of the plates is 40 mm.An electron is projected from plate A,directly toward plate B,with an initial velocity of v₀ = 1.0 × 10⁷ m/s,as shown in the figure.(e = 1.60 × 10^-19 C,
Ε₀ = 8.85 × 10^-12 C²/N • m²,m_el = 9.11 × 10^-31 kg)The distance of closest approach of the electron to plate B is nearest to

A) 16 mm.
B) 18 mm.
C) 20 mm.
D) 22 mm.
E) 24 mm.

Question 28

A very long wire carries a uniform linear charge density of 7.0 nC/m.What is the electric field strength 16.0 m from the center of the wire at a point on the wire's perpendicular bisector?
(ε₀ = 8.85 × 10^-12 C^2/N • m²)

A) 7.9 N/C
B) 3.9 N/C
C) 0.49 N/C
D) 0.031 N/C

Question 29

In the figure,a proton is projected horizontally midway between two parallel plates that are separated by 0.50 cm.The electrical field due to the plates has magnitude 610,000 N/C between the plates away from the edges.If the plates are 5.60 cm long,find the minimum speed of the proton if it just misses the lower plate as it emerges from the field.(e = 1.60 × 10^-19 C,ε₀ = 8.85 × 10^-12 C²/N • m²,
m_el = 9.11 × 10^-31 kg)

Question 30

A long,thin rod parallel to the y-axis is located at x = -1.0 cm and carries a uniform linear charge density of +1.0 nC/m.A second long,thin rod parallel to the z-axis is located at x = +1.0 cm and carries a uniform linear charge density of -1.0 nC/m.What is the net electric field due to these rods at the origin? (ε₀ = 8.85 × 10^-12 C²/N • m²)

A) (-3.6 × 10³ N/C)
B) (1.8 × 10³ N/C)
C) (-1.8 × 10³ N/C)
D) (3.6 × 10³ N/C)
E) zero

Question 31

An electric dipole consists of charges ±5.00 µC separated by 1.20 mm.It is placed in a vertical electric field of magnitude 525 N/C oriented as shown in the figure.The magnitude of the net torque this field exerts on the dipole is closest to

A) 2.02 × 10^-6 N • m.
B) 3.15 × 10^-6 N • m.
C) 2.41 × 10^-6 N • m.
D) 1.01 × 10^-6 N • m.
E) 1.21 × 10^-6 N • m.

Question 32

A thin,circular disk of radius 30.0 cm is oriented in the yz-plane with its center at the origin.The disk carries a total charge of +3.00 μC distributed uniformly over its surface.Calculate the magnitude of the electric field due to the disk at the point x = 15.0 cm along the x-axis.(ε₀ = 8.85 × 10^-12 C²/N • m²)

A) 9.95 × 10⁵ N/C
B) 4.98 × 10⁵ N/C
C) 3.31 × 10⁵ N/C
D) 2.49 × 10⁵ N/C
E) 1.99 × 10⁵ N/C

Question 33

A 3.0-μC positive point charge is located at the origin and a 2.0 μC positive point charge is located at
X = 0.00 m,y = 1.0 m. Find the coordinates of the point where the net electric field strength due to these charges is zero.

A) x = 0.00 m, y = 0.55 m
B) x = 0.00 m, y = 0.67 m
C) x = 0.00 m, y = 1.5 m
D) x = 0.00 m, y = 0.60 m

Question 34

A dipole with a positive charge of 2.0 μC and a negative charge of -2.0 μC is centered at the origin and oriented along the x-axis with the positive charge located to the right of the origin.The charge separation is 0.0010 m.Find the electric field due to this dipole at the point x = 4.0 m,y = 0.0 m.
(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

A) 0.56 N/C
B) -0.56 N/C
C) 0.28 N/C
D) -0.28 N/C