Question 1

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

Accepted Answer

The relation between electric potential (V) and electric field (E) is given by E = -dV/dx. Thus, differentiating the given potential function with respect to x, we get E = -6/x^2, since all the other terms are constants. The x component of this electric field is simply Ex = -E = 6/x^2. Multiplying by x, we get Ex = 6x^-1. Expressing this in the form 12x^-3, we can see that the correct answer is choice C, since 12 = 6*2 and -1/3 = -⁺.

Question 2

A conducting sphere 45 cm in diameter carries an excess of charge,and no other charges are present.You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity.(k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)The excess charge on this sphere is closest to

Accepted Answer

We can use the formula for the potential of a conducting sphere:

V = kQ/r

where V is the potential, Q is the charge, r is the radius/diameter of the sphere, and k is Coulomb's constant.

We can rearrange this to solve for Q:

Q = Vr/k

Substituting in the given values:

Q = (14,000 V)(0.225 m)/(8.99 x 10^9 N*m^2/C^2)

Q = 350.4 x 10^-9 C

Rounding to two significant figures, the closest answer choice is D) 350 nC.

Question 3

Two large conducting parallel plates A and B are separated by 2.4 m.A uniform field of  ,in the positive x-direction,is produced by charges on the plates.The center plane at  m is an equipotential surface on which  .An electron is projected from  ,with an initial velocity of  perpendicular to the plates in the positive x-direction,as shown in the figure.What is the kinetic energy of the electron as it reaches plate A?  ,

Accepted Answer

The answer of Two large conducting parallel plates A and...

Question 4

A charge Q = -610 nC is uniformly distributed on a ring of 2.4-m radius.A point charge is fixed at the center of the ring,as shown in the figure.An electron is projected from infinity toward the ring along the axis of the ring.This electron comes to a momentary halt at a point on the axis that is 5.0 m from the center of the ring.What is the initial speed of the electron at infinity? ,k = 1/4πε₀= ,m_el=

Accepted Answer

To solve this problem, we can use conservation of energy:

Initial kinetic energy of the electron = Final gravitational potential energy of the electron + Final electric potential energy of the electron

At infinity, the electron has zero gravitational potential energy and zero electric potential energy (since it is infinitely far away from the charged ring and point charge). Therefore:

1/2 mv_inf^2 = kQq/r + kqQ/d

where m is the mass of the electron, v_inf is the initial speed of the electron at infinity, Q is the charge on the ring, q is the charge of the electron, r is the radius of the ring, d is the distance between the ring and point charge, and k is Coulomb's constant (1/4πε₀).

We can solve for v_inf:

v_inf = sqrt[2kQq/r + 2kqQ/d]/m

Substituting in the given values and solving, we get:

v_inf = 6.6 × 10^6 m/s

Therefore, the best choice is A.

Question 5

A conducting sphere of radius 20.0 cm carries an excess charge of +15.0 µC,and no other charges are present.(k = 1/4πε₀ = The potential (relative to infinity)due to this sphere at a point 12.0 cm from its center is closest to

Accepted Answer

We can use the formula for the potential due to a charged sphere:
V = k*q/r

where V is the potential at a distance r from the center of the sphere, q is the charge on the sphere, and k is the Coulomb constant.

Substituting the given values, we get:
V = (1/4πε₀)(15.0×10⁻⁶ C)/(0.12 m) = 673.8 kV

Thus, the closest answer option is B) 674 kV.

Question 6

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).

Accepted Answer

To find the electric field vector, we need to take the gradient of the electric potential function. The gradient operator is: ∇ = î(∂/∂x) + ĵ(∂/∂y) + k^(∂/∂z) Taking the gradient of the electric potential function V(x,y,z), we get: ∇V = (3²^y²)î + (3²^x² + z³)ĵ + (-2³^x + 3yz³)k^ Now we can substitute the given values of (x,y,z)=(1.0,1.0,1.0) into this expression to get the electric field vector at that point: E = - ∇V = - (3î + 1ĵ -5k^) Taking the magnitude of E, we get: |E| = √(3^2 + 1^2 + (-5)^2) = 8.6 V/m Therefore, the correct answer is D) 8.6 V/m.

Question 7

A very long nonconducting cylinder of diameter 10.0 cm carries charge distributed uniformly over its surface.Each meter of length carries +5.50 µC of charge.A proton is released from rest just outside the surface.How far will it be from the SURFACE of the cylinder when its speed has reached 2550 km/s? (k = 1/4πε₀= , ,

Accepted Answer

The answer of A very long nonconducting cylinder of diameter...

Question 8

A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity).If the sphere's radius were twice as large,but the charge on the sphere were the same,what would be the potential on the surface relative to infinity?

Accepted Answer

The potential on the surface of a conducting sphere is given by $V = \frac{kQ}{r}$, where $V$ is the potential, $k$ is Coulomb's constant, $Q$ is the charge on the sphere, and $r$ is the radius of the sphere. Doubling the radius while keeping the charge constant halves the potential, making it 50 V.

Question 9

A charge Q = -820 nC is uniformly distributed on a ring of 2.4 m radius.A point charge is fixed at the center of the ring.Points A and B are located on the axis of the ring,as shown in the figure.What is the minimum work that an external force must do to transport an electron from B to A? ,k = 1/4πε₀ =

Accepted Answer

The answer of A charge Q = -820 nC is...

Question 10

If the potential in a region is given by V(x,y,z)= xy - 3z^-2,then the y component of the electric field in that region is

Accepted Answer

The electric field $\vec{E}$ is related to the potential $V$ by $\vec{E} = -\nabla V$, where $\nabla V$ is the gradient of $V$. The y-component of $\vec{E}$ is given by $-\frac{\partial V}{\partial y}$. For $V(x,y,z) = xy - 3z^{2}$, $-\frac{\partial V}{\partial y} = -x$, which corresponds to option C.

Question 11

An extremely long thin wire carries a uniform linear charge density of 358 nC/m.Find the potential difference between points 5.0 m and 6.0 m from the wire,provided they are not near either end of the wire.(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

Accepted Answer

The answer of An extremely long thin wire carries a...

Question 12

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?

Accepted Answer

The electric field is given by the negative gradient of the electric potential:$$\overrightarrow{E}=-
abla V = -\left(\frac{\partial V}{\partial x}\hat{x} + \frac{\partial V}{\partial y}\hat{y}ight)$$So, the electric field is zero when both partial derivatives are zero:$$\frac{\partial V}{\partial x} = 2y - 2x = 0$$$$\frac{\partial V}{\partial y} = 2x - 1 = 0$$Solving these equations simultaneously gives:$$x = 0.5 	ext{ m}$$$$y = 0.5 	ext{ m}$$Therefore, the electric field is zero at the point (0.5 m, 0.5 m).

Question 13

Two long conducting cylindrical shells are coaxial and have radii of 20 mm and 80 mm.The electric potential of the inner conductor,with respect to the outer conductor,is +600 V.An electron is released from rest at the surface of the outer conductor.What is the speed of the electron as it reaches the inner conductor?  ,  ,

Accepted Answer

The answer of Two long conducting cylindrical shells are coaxial...

Question 14

Two long conducting cylindrical shells are coaxial and have radii of 20 mm and 80 mm.The electric potential of the inner conductor,with respect to the outer conductor,is +600 V.What is the maximum electric field magnitude between the cylinders?  =

Accepted Answer

The answer of Two long conducting cylindrical shells are coaxial...

Question 15

Two parallel conducting plates are separated by  and carry equal but opposite surface charge densities.If the potential difference between them is  what is the magnitude of the surface charge density on each plate?

Accepted Answer

The answer of Two parallel conducting plates are separated by...

Quiz 23: Electric Potential

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 conducting sphere 45 cm in diameter carries an excess of charge,and no other charges are present.You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity.(k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The excess charge on this sphere is closest to

A conducting sphere of radius 20.0 cm carries an excess charge of +15.0 µC,and no other charges are present.(k = 1/4πε₀ = The potential (relative to infinity) due to this sphere at a point 12.0 cm from its center is closest to

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) .

A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity) .If the sphere's radius were twice as large,but the charge on the sphere were the same,what would be the potential on the surface relative to infinity?

If the potential in a region is given by V(x,y,z) = xy - 3z^-2,then the y component of the electric field in that region is

An extremely long thin wire carries a uniform linear charge density of 358 nC/m.Find the potential difference between points 5.0 m and 6.0 m from the wire,provided they are not near either end of the wire.(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

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?

Two long conducting cylindrical shells are coaxial and have radii of 20 mm and 80 mm.The electric potential of the inner conductor,with respect to the outer conductor,is +600 V.What is the maximum electric field magnitude between the cylinders? =

Two parallel conducting plates are separated by and carry equal but opposite surface charge densities.If the potential difference between them is what is the magnitude of the surface charge density on each plate?

Quiz 23: Electric Potential

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 conducting sphere 45 cm in diameter carries an excess of charge,and no other charges are present.You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity.(k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) The excess charge on this sphere is closest to

A conducting sphere of radius 20.0 cm carries an excess charge of +15.0 µC,and no other charges are present.(k = 1/4πε0 = The potential (relative to infinity) due to this sphere at a point 12.0 cm from its center is closest to

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 conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity) .If the sphere's radius were twice as large,but the charge on the sphere were the same,what would be the potential on the surface relative to infinity?

If the potential in a region is given by V(x,y,z) = xy - 3z-2,then the y component of the electric field in that region is

An extremely long thin wire carries a uniform linear charge density of 358 nC/m.Find the potential difference between points 5.0 m and 6.0 m from the wire,provided they are not near either end of the wire.(k = 1/4πε0 = 8.99 × 109 N • m2/C2)

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?

Two long conducting cylindrical shells are coaxial and have radii of 20 mm and 80 mm.The electric potential of the inner conductor,with respect to the outer conductor,is +600 V.What is the maximum electric field magnitude between the cylinders? =

Two parallel conducting plates are separated by and carry equal but opposite surface charge densities.If the potential difference between them is what is the magnitude of the surface charge density on each plate?

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 conducting sphere 45 cm in diameter carries an excess of charge,and no other charges are present.You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity.(k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The excess charge on this sphere is closest to

A conducting sphere of radius 20.0 cm carries an excess charge of +15.0 µC,and no other charges are present.(k = 1/4πε₀ = The potential (relative to infinity) due to this sphere at a point 12.0 cm from its center is closest to

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) .

If the potential in a region is given by V(x,y,z) = xy - 3z^-2,then the y component of the electric field in that region is

An extremely long thin wire carries a uniform linear charge density of 358 nC/m.Find the potential difference between points 5.0 m and 6.0 m from the wire,provided they are not near either end of the wire.(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

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?