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25. Electric Potential

Electric Potential

25. Electric Potential

Electric Potential

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Electric Potential

Electric Potential

Movement of Charges in Potential Fields

Movement of Charges in Potential Fields

Potential Due To Point Charges

Potential Due To Point Charges

Potential Difference Between Two Charges

Potential Difference Between Two Charges

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Anderson Video - Electric Potential Intro

Anderson Video - Electric Potential Intro

Anderson Video - Electric Potential Units

Anderson Video - Electric Potential Units

Physics - E&M: Ch 38.1 Voltage Potential Understood (9 of 24) Potential Due to Multiple Charges%%%

Physics - E&M: Ch 38.1 Voltage Potential Understood (9 of 24) Potential Due to Multiple Charges%%%

Michel van Biezen

Finding the Electric Potential due to Two Point Charges

Finding the Electric Potential due to Two Point Charges

Physics Explained

Electric Potential

Electric Potential

The Organic Chemistry Tutor

What is an Electric Potential ?

What is an Electric Potential ?

Physics Made Easy

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Practice this topic

Multiple Choice

How far from a 5μC charge will the potential be 100 V?

Multiple Choice

A −1μC and a 5μC charge lie on a line, separated by 5cm. What is the electric potential halfway between the two charges?

Multiple Choice

What is the electric potential 3.0 cm away from a

- 12 nC

Multiple Choice

- 9.0 nC

charge sits at the origin, and a

+ 18 nC

x = 2.0 cm

. At what location(s) is the potential zero?

Multiple Choice

A uniform electric field with strength

12 V / m

points from point A to point B, which are on the x-axis:

x_{A} = 45 m

x_{B} = 12 m

. What is the potential difference

V_{A} - V_{B}

Multiple Choice

A spherical balloon is charged so that the potential on its surface is

40 V

. The balloon is now deflated to half its original radius (with no loss of charge). What is the new potential on its surface?

Multiple Choice

Metal sphere A is charged until it has a potential of

200 V

. Metal sphere B is initially uncharged, and has a radius twice the radius of sphere A. A small wire is used to connect spheres A and B, so that they form one continuous equipotential surface. What is the final potential on the surface of sphere B?

Textbook Question

A thin spherical shell with radius R_1 = 3.00 cm is concentric with a larger thin spherical shell with radius R_2 = 5.00 cm. Both shells are made of insulating material. The smaller shell has charge q_1 = +6.00 nC distributed uniformly over its surface, and the larger shell has charge q_2 = -9.00 nC distributed uniformly over its surface. Take the electric potential to be zero at an infinite distance from both shells. (a) What is the electric potential due to the two shells at the following distance from their common center: (i) r=0; (ii) r=4.00 cm; (iii) r=6.00 cm?

Textbook Question

Two stationary point charges +3.00 nC and +2.00 nC are separated by a distance of 50.0 cm. An electron is released from rest at a point midway between the two charges and moves along the line connecting the two charges. What is the speed of the electron when it is 10.0 cm from the +3.00-nC charge?

Textbook Question

(a) How much excess charge must be placed on a copper sphere 25.0 cm in diameter so that the potential of its center, relative to infinity, is 3.75 kV? (b) What is the potential of the sphere's surface relative to infinity?

Textbook Question

Two large, parallel conducting plates carrying opposite charges of equal magnitude are separated by 2.20 cm. The surface charge density for each plate has magnitude 47.0 nC/m^2. (c) If the separation between the plates is doubled while the surface charge density is kept constant at the given value, what happens to the magnitude of the electric field and to the potential difference?

Textbook Question

An infinitely long line of charge has linear charge density 5.00x10^-12 C/m. A proton (mass 1.67x10^-27 kg, charge +1.60x10^-19 C) is 18.0 cm from the line and moving directly toward the line at 3.50x10^3 m/s. (a) Calculate the proton's initial kinetic energy.

Textbook Question

At a certain distance from a point charge, the poten-tial and electric-field magnitude due to that charge are 4.98 V and 16.2 V/m, respectively. (Take V = 0 at infinity.) (c) Is the electric field directed toward or away from the point charge?

Textbook Question

At a certain distance from a point charge, the poten-tial and electric-field magnitude due to that charge are 4.98 V and 16.2 V/m, respectively. (Take V = 0 at infinity.) (b) What is the magnitude of the charge?

Textbook Question

An electron is to be accelerated from 3.00x10^6 m/s to 8.00x10^6 m/s. (a) Through what potential difference must the electron pass to accomplish this?

Textbook Question

At a certain distance from a point charge, the poten-tial and electric-field magnitude due to that charge are 4.98 V and 16.2 V/m, respectively. (Take V = 0 at infinity.) (a) What is the distance to the point charge?

Textbook Question

Two point charges q_1 = +2.40 nC and q_2 = -6.50 nC are 0.100 m apart. Point A is midway between them; point B is 0.080 m from q_1 and 0.060 m from q_2 (Fig. E23.19). Take the electric potential to be zero at infinity. Find (b) the potential at point B.

Textbook Question

Two point charges q_1 = +2.40 nC and q_2 = -6.50 nC are 0.100 m apart. Point A is midway between them; point B is 0.080 m from q_1 and 0.060 m from q_2 (Fig. E23.19). Take the electric potential to be zero at infinity. Find (a) the potential at point A.

Textbook Question

Two point charges of equal magnitude Q are held a distance d apart. Consider only points on the line passing through both charges. (a) If the two charges have the same sign, find the location of all points (if there are any) at which (i) the potential (relative to infinity) is zero (is the electric field zero at these points?), and (ii) the electric field is zero (is the potential zero at these points?).

Textbook Question

Two point charges of equal magnitude Q are held a distance d apart. Consider only points on the line passing through both charges. (a) If the two charges have the same sign, find the location of all points (if there are any) at which (i) the potential (relative to infinity) is zero (is the electric field zero at these points?), and (ii) the electric field is zero (is the potential zero at these points?).

Textbook Question

Point charges q_1 = +2.00 μC and q_2 = -2.00 μC are placed at adjacent corners of a square for which the length of each side is 3.00 cm. Point a is at the center of the square, and point bis at the empty corner closest to q_2. Take the electric potential to be zero at a distance far from both charges. (a) What is the electric potential at point a due to q_1 and q_2?

Textbook Question

A small particle has charge -5.00 μC and mass 2.00x10^-4 kg. It moves from point A, where the electric po-tential is V_A = +200 V, to point B, where the electric potential is V_B = +800 V. The electric force is the only force acting on the particle. The particle has speed 5.00 m/s at point A. What is its speed at point B? Is it moving faster or slower at B than at A? Explain.

Textbook Question

BIO. Electrical Sensitivity of Sharks. Certain sharks can detect an electric field as weak as 1.0 μV/m. To grasp how weak this field is, if you wanted to produce it between two parallel metal plates by connecting an ordinary 1.5V AA battery across these plates, how far apart would the plates have to be?

Textbook Question

Two large, parallel conducting plates carrying opposite charges of equal magnitude are separated by 2.20 cm. (b) What is the potential difference between the two plates?

Textbook Question

A very long insulating cylinder of charge of radius 2.50 cm carries a uniform linear density of 15.0 nC/m. If you put one probe of a voltmeter at the surface, how far from the surface must the other probe be placed so that the voltmeter reads 175 V?

Textbook Question

An infinitely long line of charge has linear charge density 5.00x10^-12 C/m. A proton (mass 1.67x10^-27 kg, charge +1.60x10^-19 C) is 18.0 cm from the line and moving directly toward the line at 3.50x10^3 m/s. (b) How close does the proton get to the line of cha rge?

Textbook Question

FIGURE EX26.3 is a graph of Ex . What is the potential difference between xi=1.0 m and xf=3.0 m? <IMAGE>

Textbook Question

A thin rod of length L and total charge Q has the nonuniform linear charge distribution λ(x)=λ ₀x/L, where x is measured from the rod's left end. b. What is the electric potential on the axis at distance d left of the rod's left end?

Textbook Question

A 1.0-mm-diameter ball bearing has 2.0×10^9 excess electrons. What is the ball bearing's potential?

Textbook Question

CALC The electric field in a region of space is Ex=5000x V/m , where x is in meters. b. Find an expression for the potential V at position x. As a reference, let V=0 V at the origin.

Textbook Question

CALC An electric dipole at the origin consists of two charges ±q spaced distance s apart along the y-axis. a. Find an expression for the potential V(x, y) at an arbitrary point in the xy-plane. Your answer will be in terms of q, s, x, and y.

Textbook Question

INT CALC Two positive point charges q are located on the y-axis at y = ±a. a. Write an expression for the electric potential at position x on the x-axis.

FIGURE EX26.3 is a graph of Ex . What is the potential difference between x_i=1.0 m and x_f=3.0 m?

Textbook Question

CALC Use the on-axis potential of a charged disk from Chapter 25 to find the on-axis electric field of a charged disk.

Textbook Question

(II) The electric potential between two parallel conducting plates is given by V(x) = (8.5 V/m0 x + 4.5 V , with x = 0 taken at one of the plates and x positive in the direction toward the other plate. What is the charge density on the plates?

Textbook Question

(II) A dust particle with mass of 0.050 g and a charge of 2.0 x 10⁻⁶ C is in a region of space where the potential is given by V(x) = (2.0 V/m²) x² - (3.0 V/m³)x³. If the particle starts at x = 2.5m, what is the initial acceleration of the charge?

Textbook Question

A thin flat disk of radius R₀ carries a total charge Q that is distributed uniformly over its surface. The electric potential at a distance x on the x axis is given by

V(x) = Q/ 2π∊₀R²₀ [(x² + R²₀) ¹⸍² - x] .

(See Example 23–10.) Show that the electric field at a distance x on the x axis is given by

E(x) = Q/2π∊₀R²₀ ( 1 - ( x / ( x² + R²₀))¹⸍² .

Make graphs of V(x) and E(x) as a function of x/R₀ for x/R₀ = 0 to 4. (Do the calculations in steps of 0.1.) Use Q = 5.0μC and R₀ = 10cm for the calculation and graphs.

Textbook Question

(I) How much work does the electric field do in moving a - 9.7 μC charge from ground to a point whose potential is + 65V higher?

Textbook Question

(I) An electron acquires 4.665 x 10⁻¹⁶ J of kinetic energy when it is accelerated by an electric field from plate A to plate B. What is the potential difference between the plates, and which plate is at the higher potential?

Textbook Question

(II) The work done by an external force to move a - 7.40 μC charge from point A to point B is 15.0 x 10⁻⁴ J. If the charge was started from rest and had 4.82 x 10⁻⁴ J of kinetic energy when it reached point B, what must be the potential difference between A and B?

Textbook Question

(II) What minimum radius must a large conducting sphere (of an electrostatic generating machine) have if it is to be at 45,000 V without discharge into the air? How much charge will it carry?

Textbook Question

(II) A 32-cm-diameter conducting sphere is charged to 480 V relative to V = 0 at r = ∞ .

(a) What is the surface charge density σ?

(b) At what distance will the potential due to the sphere be only 25 V?

Textbook Question

(II) Suppose the end of your finger is charged.

(a) Estimate the breakdown voltage in air for your finger.

(b) About what surface charge density would have to be on your finger at this voltage?

Textbook Question

(III) A very long conducting cylinder (length ℓ) of radius R₀ (R₀ ≪ ℓ) carries a uniform surface charge density σ (C/m²) . The cylinder is at an electric potential V₀ . Determine the potential, at points far from the end, at a distance R from the center of the cylinder for

(a) R > R₀ and (b) R < R₀ .

(c) Is V = 0 at R = ∞ (assume ℓ = ∞ )? Explain. [Hint: Recall Gauss’s law.]

Textbook Question

(II) A total charge Q is uniformly distributed on a thread of length ℓ . The thread forms a semicircle. What is the potential at the full-circle’s center? (Assume V = 0 at large distances.)

Textbook Question

(II) Calculate the electric potential due to a tiny dipole whose dipole moment is 4.8 x 10⁻³⁰ C·m at a point 4.1 x 10⁻⁹ m away if this point is

(a) along the axis of the dipole nearer the positive charge;

Textbook Question

(II) Calculate the electric potential due to a tiny dipole whose dipole moment is 4.8 x 10⁻³⁰ C·m at a point 4.1 x 10⁻⁹ m away if this point is

(b) 45° above the axis but nearer the positive charge;

Textbook Question

A lightning flash transfers 4.0 C of charge and 5.2 MJ of energy to the Earth.

(a) Across what potential difference did it travel?

Textbook Question

(II) A thin rod of length 2ℓ is centered on the x axis as shown in Fig. 23–46. The rod carries a uniformly distributed charge Q. Determine the potential V as a function of y for points along the y axis. Let V = 0 at infinity.

<IMAGE>

Textbook Question

A hollow cylindrical shell of length L and radius R has charge Q uniformly distributed along its length. What is the electric potential at the center of the cylinder?

Textbook Question

CALC Consider a uniformly charged sphere of radius R and total charge Q. The electric field Eout outside the sphere (r≥R) is simply that of a point charge Q. In Chapter 24, we used Gauss’s law to find that the electric field Ein inside the sphere (r≤R) is radially outward with field strength Ein = 1 Q 4πϵ0 R^3 r b. What is the ratio Vcenter /Vsurface?

Textbook Question

In the Bohr model of the hydrogen atom, an electron orbits a proton (the nucleus) in a circular orbit of radius 0.53 x 10⁻¹⁰ m .

(a) What is the electric potential at the electron’s orbit due to the proton?

Textbook Question

(II) In the commonly used “ASCII” code, numbers, letters and other symbols are stored as 8-digit binary numbers. The code for the letter A is 00100001, and the next letters are just the next binary numbers.

(b) What would be the decimal numbers for ASCII B and H?

<IMAGE>

Textbook Question

(II) A uniform electric field E→ = -6.30 N/Cî points in the negative x direction as shown in Fig. 23–40. The x and y coordinates of points A, B, and C are given on the diagram (in meters). Determine the differences in potential

(a) V_BA ,

<IMAGE>

Textbook Question

(II) A uniform electric field E→ = -6.30 N/Cî points in the negative x direction as shown in Fig. 23–40. The x and y coordinates of points A, B, and C are given on the diagram (in meters). Determine the differences in potential

(b) V_CB , and

<IMAGE>

Textbook Question

(II) Point a is 26 cm north of a -3.8 μC point charge, and point b is 36 cm west of the charge (Fig. 23–43). Determine

(a) Vᵦ - Vₐ, and

<IMAGE>

Textbook Question

The potential in a region of space is given by V = B / ( x² + R²)² where B = 120 V•m⁴ and R = 0.20 m . (a) Find V at x = 0.20 m. (b) Find E→ as a function of x. (c) Find E→ at x = 0.20 m.

Showing 57 of 57 practice