In a certain region,the electric potential due to a charge distribution is given by the equation V(x,y)= 2xy - x2 - y,where x and y are measured in meters and V is in volts.At which point is the electric field equal to zero?

A) x = 0.5 m,y = 1 m B) x = 1 m,y = 1 m C) x = 1 m,y = 0.5 m D) x = 0.5 m,y = 0.5 m E) x = 0 m,y = 0 m A) x = 0.5 m,y = 1 m B) x = 1 m,y = 1 m C) x = 1 m,y = 0.5 m D) x = 0.5 m,y = 0.5 m E) x = 0 m,y = 0 m

In a certain region,the electric potential due to a charge distribution is given by the equation V(x,y,z)= 3x2y2 + yz3 - 2z3x,where x,y,and z are measured in meters and V is in volts.Calculate the magnitude of the electric field vector at the position (x,y,z)= (1.0,1.0,1.0).

A) 4.3 V/m B) 2.0 V/m C) -8.1 V/m D) 8.6 V/m E) 74 V/m A) 4.3 V/m B) 2.0 V/m C) -8.1 V/m D) 8.6 V/m E) 74 V/m

If the electric potential in a region is given by V(x)= 6/x2,the x component of the electric field in that region is

A) -12x-3. B) -6x. C) 12x-3. D) 12x. E) 6x. A) -12x-3. B) -6x. C) 12x-3. D) 12x. E) 6x.

The four identical capacitors in the circuit shown in the figure are initially uncharged.Let the charges on the capacitors be Q1,Q2,Q3,and Q4 and the potential differences across them be V1,V2,V3,and V4.The switch is thrown first to position A and kept there for a long time.It is then thrown to position B.Which of the following conditions is true with the switch in position B?

A) V1 = V2 = V3 = V4 B) V1 = V0 C) V1 + V2 + V3 + V4 = V0 D) Q1 = 3 Q2 E) Q1 = Q2 A) V1 = V2 = V3 = V4 B) V1 = V0 C) V1 + V2 + V3 + V4 = V0 D) Q1 = 3 Q2 E) Q1 = Q2

Exam 26: Potential and Field

Equal but opposite charges Q are placed on the square plates of an air-filled parallel-plate capacitor.The plates are then pulled apart to twice their original separation,which is small compared to the dimensions of the plates.Which of the following statements about this capacitor are true? (There may be more than one correct choice.)

(Multiple Choice)

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Question 41

A 6.0-μF air-filled capacitor is connected across a 100-V voltage source.After the source fully charges the capacitor,the capacitor is immersed in transformer oil (of dielectric constant 4.5).How much ADDITIONAL charge flows from the voltage source,which remained connected during the process?

(Multiple Choice)

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Question 42

When two or more capacitors are connected in series across a potential difference,

(Multiple Choice)

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Question 43

In a certain region,the electric potential due to a charge distribution is given by the equation V(x,y)= 2xy - x² - y,where x and y are measured in meters and V is in volts.At which point is the electric field equal to zero?

(Multiple Choice)

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Question 44

In a certain region,the electric potential due to a charge distribution is given by the equation V(x,y,z)= 3x²^y² + yz³ - 2z³^x,where x,y,and z are measured in meters and V is in volts.Calculate the magnitude of the electric field vector at the position (x,y,z)= (1.0,1.0,1.0).

(Multiple Choice)

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Question 45

An ideal parallel-plate capacitor consists of a set of two parallel plates of area A separated by a very small distance d.When the capacitor plates carry charges +Q and -Q,the capacitor stores energy U₀.If the separation between the plates is doubled,how much electrical energy is stored in the capacitor?

(Multiple Choice)

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Question 46

In the circuit shown in the figure,the capacitors are initially uncharged.The switch is first thrown to position A and kept there for a long time.It is then thrown to position B.Let the charges on the capacitors be Q₁,Q₂,and Q₃ and the potential differences across them be V₁,V₂,and V₃.Which of the following conditions must be true with the switch in position B?

(Multiple Choice)

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Question 47

A parallel-plate capacitor has a capacitance of 10 mF and is charged with a 20-V power supply.The power supply is then removed and a dielectric material of dielectric constant 4.0 is used to fill the space between the plates.What is the voltage now across the capacitor?

(Multiple Choice)

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Question 48

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates.All the geometric parameters of the capacitor (plate diameter and plate separation)are now DOUBLED.If the original capacitance was C₀,what is the new capacitance?

(Multiple Choice)

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Question 49

If the electric potential in a region is given by V(x)= 6/x²,the x component of the electric field in that region is

(Multiple Choice)

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Question 50

Each plate of an air-filled parallel-plate air capacitor has an area of 0.0040 m²,and the separation of the plates is 0.080 mm.An electric field of 5.3 × 10⁶ V/m is present between the plates.What is the energy density between the plates? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

(Multiple Choice)

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Question 51

The four identical capacitors in the circuit shown in the figure are initially uncharged.Let the charges on the capacitors be Q₁,Q₂,Q₃,and Q₄ and the potential differences across them be V₁,V₂,V₃,and V₄.The switch is thrown first to position A and kept there for a long time.It is then thrown to position B.Which of the following conditions is true with the switch in position B?

(Multiple Choice)

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Question 52

A parallel-plate capacitor has plates of area 0.40 m² and plate separation of 0.20 mm.The capacitor is connected across a 9.0-V potential source.(ε₀ = 8.85 × 10^-12 C²/N ∙ m²) (a)What is the magnitude of the electric field between the plates? (b)What is the capacitance of the capacitor? (c)What is the magnitude of the charge on each plate of the capacitor?

(Essay)

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Question 53

A metallic sphere of radius 5 cm is charged such that the potential of its surface is 100 V (relative to infinity).Which of the following plots correctly shows the potential as a function of distance from the center of the sphere?

(Multiple Choice)

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Question 54

The capacitive network shown in the figure is assembled with initially uncharged capacitors.A potential difference,V_ab = +100V,is applied across the network.The switch S in the network is initially open but is then closed.Assume that all the capacitances shown are accurate to two significant figures.What is the equivalent capacitance between ab (a)with the switch S open? (b)with the switch S closed?

(Short Answer)

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Question 55

Four capacitors are connected across a 90-V voltage source as shown in the figure. (a)What is the charge on the 4.0-μF capacitor? (b)What is the charge on a 2.0-μF capacitor? (c)What is the charge on the 3.0-μF capacitor? (d)What is the potential difference across the 6.0-μF capacitor?

(Essay)

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Question 56

A 15-μF air-filled capacitor is connected to a 50-V voltage source and becomes fully charged.The voltage source is then removed and a slab of dielectric that completely fills the space between the plates is inserted.The dielectric has a dielectric constant of 5.0. (a)What is the capacitance of the capacitor after the slab has been inserted? (b)What is the potential difference across the plates of the capacitor after the slab has been inserted?

(Short Answer)

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Question 57

Showing 41 - 57 of 57

Exam 26: Potential and Field

A 6.0-μF air-filled capacitor is connected across a 100-V voltage source.After the source fully charges the capacitor,the capacitor is immersed in transformer oil (of dielectric constant 4.5).How much ADDITIONAL charge flows from the voltage source,which remained connected during the process?

When two or more capacitors are connected in series across a potential difference,

In a certain region,the electric potential due to a charge distribution is given by the equation V(x,y)= 2xy - x2 - y,where x and y are measured in meters and V is in volts.At which point is the electric field equal to zero?

In a certain region,the electric potential due to a charge distribution is given by the equation V(x,y,z)= 3x2y2 + yz3 - 2z3x,where x,y,and z are measured in meters and V is in volts.Calculate the magnitude of the electric field vector at the position (x,y,z)= (1.0,1.0,1.0).

A parallel-plate capacitor has a capacitance of 10 mF and is charged with a 20-V power supply.The power supply is then removed and a dielectric material of dielectric constant 4.0 is used to fill the space between the plates.What is the voltage now across the capacitor?

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates.All the geometric parameters of the capacitor (plate diameter and plate separation)are now DOUBLED.If the original capacitance was C0,what is the new capacitance?

If the electric potential in a region is given by V(x)= 6/x2,the x component of the electric field in that region is

Each plate of an air-filled parallel-plate air capacitor has an area of 0.0040 m2,and the separation of the plates is 0.080 mm.An electric field of 5.3 × 106 V/m is present between the plates.What is the energy density between the plates? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

A metallic sphere of radius 5 cm is charged such that the potential of its surface is 100 V (relative to infinity).Which of the following plots correctly shows the potential as a function of distance from the center of the sphere?

Four capacitors are connected across a 90-V voltage source as shown in the figure. (a)What is the charge on the 4.0-μF capacitor? (b)What is the charge on a 2.0-μF capacitor? (c)What is the charge on the 3.0-μF capacitor? (d)What is the potential difference across the 6.0-μF capacitor?

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In a certain region,the electric potential due to a charge distribution is given by the equation V(x,y)= 2xy - x² - y,where x and y are measured in meters and V is in volts.At which point is the electric field equal to zero?

In a certain region,the electric potential due to a charge distribution is given by the equation V(x,y,z)= 3x²^y² + yz³ - 2z³^x,where x,y,and z are measured in meters and V is in volts.Calculate the magnitude of the electric field vector at the position (x,y,z)= (1.0,1.0,1.0).

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates.All the geometric parameters of the capacitor (plate diameter and plate separation)are now DOUBLED.If the original capacitance was C₀,what is the new capacitance?

If the electric potential in a region is given by V(x)= 6/x²,the x component of the electric field in that region is

Each plate of an air-filled parallel-plate air capacitor has an area of 0.0040 m²,and the separation of the plates is 0.080 mm.An electric field of 5.3 × 10⁶ V/m is present between the plates.What is the energy density between the plates? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)