Question 1

If a charge of 12 μC is located 5.0 cm from a charge of 6.5 μC, the potential energy of this arrangement is

Accepted Answer

The answer of If a charge of 12 μC is...

Question 2

If an electron is accelerated from rest through a potential difference of 25,000 volts in a color television picture tube, its kinetic energy will be

Accepted Answer

The kinetic energy gained by an electron accelerated through a potential difference V is given by the equation KE = eV, where e is the charge of the electron (1.6 × 10^-19 C). For V = 25,000 volts, KE = 1.6 × 10^-19 C × 25,000 V = 4.0 × 10^-15 J.

Question 3

Two point charges q₁ = 4.0 μC and q₂ = -8.0 μC are placed along the x-axis at x₁ = 0 m and x₂ = 0.20 m, respectively. What is the electric potential energy of this system of charges?

Accepted Answer

The electric potential energy (U) of a system of point charges is given by:
U = kq1q2/r
where k is Coulomb's constant (9x10^9 Nm^2/C^2), q1 and q2 are the charges of the two point charges (in coulombs), and r is the distance between the charges (in meters).

In this case, q1 = 4.0 μC, q2 = -8.0 μC, and r = 0.20 m. Plugging these values into the equation above, we get:
U = (9x10^9 Nm^2/C^2)(4.0x10^-6 C)(-8.0x10^-6 C)/(0.20 m)
U = -1.4 J
The negative sign indicates that the potential energy is negative, which makes sense since the two charges have opposite signs and therefore attract each other.

Question 4

The electric potential of a charge distribution is given by the equation V(x) = 3 x² y² + y z³ - 2 z³x, where x, y, z are measured in meters and V is measured in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0).

Accepted Answer

The electric field vector is given by the negative gradient of the electric potential:$$\overrightarrow{E} = -
abla V = -\left(\frac{\partial V}{\partial x}\hat{x} + \frac{\partial V}{\partial y}\hat{y} + \frac{\partial V}{\partial z}\hat{z}ight)$$Plugging in the given electric potential, we get:$$\overrightarrow{E} = -6xy^2\hat{x} - 6x^2y\hat{y} - (3y^2z^2 + 6xz^2)\hat{z}$$At the position (x,y,z) = (1.0, 1.0, 1.0), the electric field vector becomes:$$\overrightarrow{E} = -6(1.0)(1.0)^2\hat{x} - 6(1.0)^2(1.0)\hat{y} - (3(1.0)^2(1.0)^2 + 6(1.0)(1.0)^2)\hat{z}$$$$\overrightarrow{E} = -6\hat{x} - 6\hat{y} - 9\hat{z}$$The magnitude of the electric field vector is:$$|\overrightarrow{E}| = \sqrt{(-6)^2 + (-6)^2 + (-9)^2} = \sqrt{81} = 9 V/m$$Therefore, the correct answer is D) 8.6 V/m.

Question 5

If the potential is given by V = xy - 3 z^-2, then the electric field has a y-component of

Accepted Answer

The y-component of the electric field is given by the negative partial derivative of the potential V with respect to y. Thus, E_y = -∂V/∂y = -x.

Question 6

If a particle with a charge of 2 coulombs moves through a potential difference of 12 volts, its change in kinetic energy will a have magnitude of

Accepted Answer

The change in kinetic energy of a charged particle moving through a potential difference is given by the formula ΔKE = qV, where q is the charge and V is the potential difference. Here, ΔKE = 2 C * 12 V = 24 J.

Question 7

If an electron is accelerated through a potential difference of 500 V between two parallel plates separated by a distance of 2.0 cm. The change in kinetic energy of the electron during this motion is

Accepted Answer

The change in kinetic energy of an electron accelerated through a potential difference V is equal to the charge of the electron multiplied by the potential difference, which is 500 eV in this case.

Question 8

The electric potential of a charge distribution is given by V(x, y) = 2xy - x² - y. At which point is the electric field equal to zero?

Accepted Answer

The electric field is zero where the gradient of the potential is zero. The partial derivatives are ∂V/∂x = 2y - 2x and ∂V/∂y = 2x - 1. Setting these to zero gives x = 0.5 and y = 0.5.

Question 9

Three equal charges of magnitude + 4.00 μC are placed at the corners of an equilateral triangle of side 2.00 cm. What is the electric potential energy of the system of these charges?

Accepted Answer

The answer of Three equal charges of magnitude + 4.00...

Question 10

An electron is accelerated from rest through a potential difference of 1000 volts giving it a kinetic energy of

Accepted Answer

When an electron is accelerated through a potential difference of 1000 volts, it gains kinetic energy equal to the charge of the electron (1.6 × 10^-19 C) multiplied by the potential difference (1000 V), which equals 1.6 × 10^-16 J.

Quiz 23: Electric Potential

If a charge of 12 μC is located 5.0 cm from a charge of 6.5 μC, the potential energy of this arrangement is

If an electron is accelerated from rest through a potential difference of 25,000 volts in a color television picture tube, its kinetic energy will be

Two point charges q₁ = 4.0 μC and q₂ = -8.0 μC are placed along the x-axis at x₁ = 0 m and x₂ = 0.20 m, respectively. What is the electric potential energy of this system of charges?

The electric potential of a charge distribution is given by the equation V(x) = 3 x² y² + y z³ - 2 z³x, where x, y, z are measured in meters and V is measured in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0) .

If the potential is given by V = xy - 3 z^-2, then the electric field has a y-component of

If a particle with a charge of 2 coulombs moves through a potential difference of 12 volts, its change in kinetic energy will a have magnitude of

If an electron is accelerated through a potential difference of 500 V between two parallel plates separated by a distance of 2.0 cm. The change in kinetic energy of the electron during this motion is

The electric potential of a charge distribution is given by V(x, y) = 2xy - x² - y. At which point is the electric field equal to zero?

Three equal charges of magnitude + 4.00 μC are placed at the corners of an equilateral triangle of side 2.00 cm. What is the electric potential energy of the system of these charges?

An electron is accelerated from rest through a potential difference of 1000 volts giving it a kinetic energy of

Quiz 23: Electric Potential

If a charge of 12 μC is located 5.0 cm from a charge of 6.5 μC, the potential energy of this arrangement is

If an electron is accelerated from rest through a potential difference of 25,000 volts in a color television picture tube, its kinetic energy will be

Two point charges q1 = 4.0 μC and q2 = -8.0 μC are placed along the x-axis at x1 = 0 m and x2 = 0.20 m, respectively. What is the electric potential energy of this system of charges?

The electric potential of a charge distribution is given by the equation V(x) = 3 x2 y2 + y z3 - 2 z3x, where x, y, z are measured in meters and V is measured in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0) .

If the potential is given by V = xy - 3 z-2, then the electric field has a y-component of

If a particle with a charge of 2 coulombs moves through a potential difference of 12 volts, its change in kinetic energy will a have magnitude of

If an electron is accelerated through a potential difference of 500 V between two parallel plates separated by a distance of 2.0 cm. The change in kinetic energy of the electron during this motion is

The electric potential of a charge distribution is given by V(x, y) = 2xy - x2 - y. At which point is the electric field equal to zero?

Three equal charges of magnitude + 4.00 μC are placed at the corners of an equilateral triangle of side 2.00 cm. What is the electric potential energy of the system of these charges?

An electron is accelerated from rest through a potential difference of 1000 volts giving it a kinetic energy of

Two point charges q₁ = 4.0 μC and q₂ = -8.0 μC are placed along the x-axis at x₁ = 0 m and x₂ = 0.20 m, respectively. What is the electric potential energy of this system of charges?

The electric potential of a charge distribution is given by the equation V(x) = 3 x² y² + y z³ - 2 z³x, where x, y, z are measured in meters and V is measured in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0) .

If the potential is given by V = xy - 3 z^-2, then the electric field has a y-component of

The electric potential of a charge distribution is given by V(x, y) = 2xy - x² - y. At which point is the electric field equal to zero?