Exam 16: The Electric Field

Each plate of a parallel-plate air-filled capacitor has an area of 0.0040 $m ^ { 2 }$ ,and the separation of the plates is $0.020 \mathrm {~mm}$ An $\vec { E }$ field with a magnitude of $8.2 \times 10^6 \mathrm {~N} / \mathrm { C }$ is present between the plates.What is the energy density in the region between the plates? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

When a 6.00-μF air-filled capacitor has a charge of ±40.0 μC on its plates,how much potential energy is stored in this capacitor?

Consider a uniform horizontal $\vec { E }$ field of 50 N/C directed toward the east.If the electric potential measured at a given point is 80 V,what is the potential at a point 1.0 m directly west of that point?

What is the $\vec { E }$ field 2.8 cm from a tiny object that carries an excess charge of -16 nC? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Three point charges are placed at the following points in a horizontal x-y plane: $+ 4.0 \mu \mathrm { C }$ is at $( 0.00 \mathrm {~m} , 0.50 \mathrm {~m} )$ $+ 1.0 \mu \mathrm { C }$ is at $( 0.20 \mathrm {~m} , 0.00 \mathrm {~m} )$ and $- 5.0 \times \mu C$ is at $( 0.20 \mathrm {~m} , 0.50 \mathrm {~m} )$ Calculate the electrical potential (relative to infinity)at the origin due to these three point charges.(k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Consider a uniform horizontal $\vec { E }$ field of 50 N/C directed toward the east.If the electric potential at a given point in the field is 80 V,what is the potential at a point 1.0 m directly east of the point?

An ideal air-filled parallel-plate capacitor with horizontal plates has a plate separation of 5.0 cm.If the potential difference between the plates is 2000 V,with the top plate at the higher potential,what are the magnitude and direction of the $\vec { E }$ field between the plates?

An ideal air-filled parallel-plate capacitor consists of two circular plates,each of radius $0.30 \mathrm {~mm}$ How far apart should the plates be for the capacitance to be 300.0-pF? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A 5.0 μF capacitor has a potential difference of $5.0 \mathrm {~V}$ applied across its plates.If the potential difference across its plates is increased to $8.0 \mathrm {~V} ,$ how much additional energy does the capacitor store?

Two parallel square metal plates,8.4 cm on each side,are 2.5 mm apart and carry equal but opposite charge uniformly distributed over their facing surfaces.How much excess charge is there on each plate if the $\vec { E }$ field between the plates has a magnitude of 2.0 × 10⁶ N/C? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A 12.0-V battery (potential source)is connected across a 6.00-µF air-filled capacitor. (a)How much energy can be stored this way? (b)How much excess charge is on each plate of the capacitor?

Four point charges of magnitude 6.00 μC and are at the corners of a square 2.00 m on each side.Two of the charges are positive,and two are negative.What is the electric potential at the center of this square,relative to infinity,due to these charges? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Two tiny particles having charges +20.0 μC and -8.00 μC are separated by a distance of 20.0 cm.What are the magnitude and direction of the $\vec { E }$ field midway between these two charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A +5.0-μC point charge is placed at the 0 cm mark of a meter stick and a -4.0-μC charge is placed at the 50 cm mark.What is the net $\vec { E }$ field at the 30 cm mark? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A proton that is initially at rest is accelerated through an electric potential difference of magnitude 500 V.What speed does the proton gain? (e = 1.60 × 10^-19 C ,m_proton = 1.67 × 10^-27 kg)

An electron is projected with an initial velocity v₀ = 8.4 × $10^7$ m/s along the y-axis,which is the centerline between a pair of charged plates,as shown in the figure.The plates are 1.0 m long and are separated by 0.10 m.A uniform $\vec { E }$ field of known magnitude in the +x-direction is present between the plates.If the magnitude of the acceleration of the electron is measured to be $8.9 \times 10 ^ { 15 } \mathrm {~m} / \mathrm { s } ^ { 2 }$ what is the magnitude of the $\vec { E }$ field between the plates? (e = 1.6 × 10^-19 C,m_electron = 9.11 × 10^-31 kg)

When the potential difference between the plates of an ideal air-filled parallel plate capacitor is 35 V,the $\vec { E }$ field between the plates is 750 V/m.If the plate area is 4.0 × 10^-2 m²,what is the capacitance of this capacitor? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

The plates of a parallel-plate capacitor are maintained with constant potential by a battery as they are pulled apart.During this process,the amount of charge on the plates

The square plates of a 3000-pF parallel-plate capacitor measure 40 mm by 40 mm and are separated by a dielectric that is 0.29 mm thick and completely fills the region between the plates.What is the dielectric constant of the dielectric? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

If the electric potential at a point in space is zero,then the $\vec { E }$ field at that point must be