Exam 25: Electric Potential

A charge of 20 nC is distributed uniformly along the x axis from x = −2.0 m to x = +2.0 m.What is the electric potential (relative to zero at infinity)at the point x = 5.0 m on the x axis?

A linear charge of nonuniform density λ = bx,where b = 2.1 nC/m²,is distributed along the x axis from x = 2.0 m to x = 3.0 m.Determine the electric potential (relative to zero at infinity)of the point y = 4.0 m on the y axis.

Identical point charges (+50 μC)are placed at the corners of a square with sides of 2.0-m length.How much external energy is required to bring a fifth identical charge from infinity to the geometric center of the square?

A +4.0-μC charge is placed on the x axis at x = +3.0 m,and a −2.0-μC charge is located on the y axis at y = −1.0 m.Point A is on the y axis at y = +4.0 m.Determine the electric potential at point A (relative to zero at the origin).

A proton (mass = 1.67 × 10−²⁷ kg,charge = 1.60 × 10−¹⁹ C)moves from point A to point B under the influence of an electrostatic force only.At point A the proton moves with a speed of 60 km/s.At point B the speed of the proton is 80 km/s.Determine the potential difference V_B − V_A.

Two charges lie on the x axis,+3q at the origin,and −2q at x = 5.0 m.The point on the x axis where the electric potential has a zero value (when the value at infinity is also zero)is

To recharge a 12-V battery,a battery charger must move 3.6 × 10⁵ C of charge from the negative to the positive terminal.What amount of work is done by the battery charger? How many kilowatt hours is this?

A charged particle (q = −8.0 mC),which moves in a region where the only force acting on the particle is an electric force,is released from rest at point A.At point B the kinetic energy of the particle is equal to 4.8 J.What is the electric potential difference V_B − V_A?

A charge of uniform density (0.80 nC/m)is distributed along the x axis from the origin to the point x = 10 cm.What is the electric potential (relative to zero at infinity)at a point,x = 18 cm,on the x axis?

A system consisting of a positively-charged particle and an electric field

Charge of uniform density 90 nC/m³ is distributed throughout the inside of a long nonconducting cylindrical rod (radius = 2.0 cm).Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod)and point B (4.0 cm from the axis).

The gap between electrodes in a spark plug is 0.06 cm.In order to produce an electric spark in a gasoline-air mixture,the electric field must reach a value of 3 × 10⁶ V/m.What minimum voltage must be supplied by the ignition circuit when starting the car?

A particle (m = 2.0 μg,q = −5.0 μC)has a speed of 30 m/s at point A and moves (with only electric forces acting on it)to point B where its speed is 80 m/s.Determine the electric potential difference V_A − V_B.

Four identical point charges (+6.0 nC)are placed at the corners of a rectangle which measures 6.0 m × 8.0 m.If the electric potential is taken to be zero at infinity,what is the potential at the geometric center of this rectangle?

How much electrical charge is needed to raise an isolated metal sphere of radius 1.0 m to a potential of 1.0 × 10⁶ V?

A particle (charge = 5.0 μC)is released from rest at a point x = 10 cm.If a 5.0-μC charge is held fixed at the origin,what is the kinetic energy of the particle after it has moved 90 cm?

What is the speed of a proton that has been accelerated from rest through a potential difference of 4.0 kV?