Electric Field Practice Problems

Two tiny balls charged to +5.1 μC and +7.21 μC are used for an electrostatics experiment.  They are joined together using a massless non-conducting rod 3.21 cm long. The +5.1 μC charged ball is fixed in place while the other charged ball is free. The assembly lies in a region of an even electric field with a magnitude of 2.0 × 10⁸ N/C.  Determine the tension/compression in the connecting rod. Model the balls as point charges.

Two tiny charged spheres (may be modeled as point charges) are connected using a massless non-conducting rod of length 3.21 cm. One sphere has a charge of -5.1 μC whereas the other has a charge of +7.21μC. The sphere of charge -5.1μC has a fixed position while the other is free. The assembly is placed in an even external electric field of magnitude 2.0 × 10⁸ N/C. What is the tension in the rod?

Two small spheres separated by a distance 2d lie on the x-axis. Each sphere carries a positive charge q. The origin of the x-axis lies at the midpoint of the two charges. What is the electric field magnitude and direction at the origin? Treat the spheres like point charges.

An extremely long linear bar is charged by friction to 1.60 nC/m. The electric field has a magnitude of 6.40 N/C at a point R measured from the bar. Determine the value of R.

Four tiny spheres are charged to some charge value of "q". They are assembled to form a square with each side a length of "d". Half of the spheres are positively charged while the other half is negatively charged. Find the magnitude (in terms of q and d) and the direction of the electric field created by the four spheres at the center of the square. Assume that these tiny balls behave like point charges.

Three charges q₁, q₂, and q₃ are located on the x-y frame as shown in the figure below. Determine the magnitude and the direction of the electric field (E) at point P. Hint: The direction of the electric field is expressed by the counterclockwise angle that E makes with the positive x-axis.

On the xy-plane, a charge q₁ = 5.0 nC is located at (0 cm, 4.0 cm) and another charge q₂ is situated along the y-axis in the negative direction. At a point P (4.0 cm, 0 cm), the electric field is determined to be 4.5 × 10⁴ N/C in the negative y-direction. Determine the position of charge q₂ in the xy-plane.

The figure below shows a thin bar of length 8.0 cm, uniformly charged with a total charge of -5.0 nC. Determine the magnitude of the electric field at point A located at a distance of 4.0 cm from the top face of the bar.

A ring with diameter D has a total charge q distributed uniformly along its circumference. The ring is centered at the origin of the x-z plane. Determine the distance from the origin, along the y-axis, at which the magnitude of the electric field is maximum.

A charge q is distributed uniformly across the thin circumference of a half of a ring with radius r as shown in the figure below. Determine the electric field in terms of q and r at the center of the ring.

A flat sheet of metal with an infinite surface is perforated at its center with a circular cavity of radius 15 cm. The surface of the metal sheet has a uniform surface charge density of 450 nC/m². Determine the magnitude of the electric field at a point directly above the center of the cavity, 20 cm away from the surface of the metal sheet.

A surface with a width W extending from y=-W/2 to y=+W/2 has an infinite length along the z-axis. It has a positive charge density σ. Illustrate the field strength E _y between y = 2W and y = 5W.

The center of a straight wire with length d is located at the origin of an x-y plane, and the wire is aligned along the x-axis. The wire's linear charge density is positive and nonuniform and given by λ=b|x|, where b is a constant with the units C/m² and x is the distance from the wire's center. Find the magnitude of the electric field at distance y on the y-axis. Hint: Start by calculating b in terms of Q and d. 

Two thin bars of length 12 cm are placed vertically in the same plane with a distance of 6.0 cm between their centers. The bars' centers lie on the same horizontal line. The left bar is uniformly charged to +0.15 μC and the right is uniformly charged to -0.15 μC. Determine the magnitude of the electric field at a point located on the line connecting the midpoints of both bars, which is positioned 2.0 cm to the right of the left bar.

Two horizontal thin metallic bars, each 24 cm in length, are separated by a distance of 8.0 cm. The bars' centers lie on the same vertical line. Both bars carry a uniformly distributed negative charge of -15 nC. Determine the magnitude of the electric field at points A and B, which lie on the line connecting the midpoints of both bars and at a distance of 2.0 cm and 4.0 cm (upward) from the lowest bar, respectively.

A flat circular object with negligible thickness has a radius of 7.5 cm. The object is made of aluminum and has been negatively charged to 5.2 nC. Assuming the charge is evenly distributed across its surface, determine the electric field's magnitude and direction at a point 0.2 mm directly above the center of the object's top surface.

Two charges are assembled as shown. Calculate the electric field magnitude and direction at point p. Give direction as a CCW angle measured from an x-axis.

Calculate the electric field's magnitude at the center point between two identical charged rings, each with a diameter of 5.0 cm and positioned 20 cm apart. The two rings face each other and hold a charge of 15 nC.

An 82 mm radius hollow sphere with a charge of -310 μC and another hollow sphere of the same size carrying a +310 μC charge is placed 240 mm apart as shown below. Determine the magnitude and direction of the electric field halfway between both spheres.

Given the linear charge density λ, for the scenario depicted in the figure below which shows a cross-section of two indefinitely long uniformly charged thin wires along the z-axis, derive a formula for the magnitude of the electric field E at a height s above the center point situated between these charged wires.

A -5.00 nC charge is placed at (3.0 cm, 1.5 cm) on an x-y plane. Determine the coordinates of a point where the electric field is (-15000i + 17000j) N/C.

A 20 g non-conducting cuboid lying at rest on a 25 degrees incline has a total charge of 8.0 × 10^-6 C. The friction coefficients between the cuboid and the incline are µ_s = 0.15 and µ_k = 0.080. If the setup lies in a horizontal electric field, what least electric field strength is required to keep the cuboid from sliding?

An electric field of magnitude 300,000 N/C pushes a charged sphere of mass 3.2 g and charge 42 nC suspended by a thread, displacing it by θ degrees from the vertical. Find the value of θ.

A 0.15 kg sparrow accumulates a +12 nC charge while perching on a power line. Determine the electric field (magnitude and direction) required for the sparrow to maintain its position in mid-air without flapping its wings.

In a laboratory experiment, a tiny plastic sphere with a charge of -8.0 nC is located at (x, y) = (2.0 cm, 0.0 cm). What is the electric field at the positions A (x, y) = (0.0 cm, 4.0 cm)? Determine the component form of the electric field vector at this position.

A water droplet of mass m and charge q is placed between two parallel plates with a downward electric field. The droplet is negatively charged. When a certain potential difference is applied, it creates an electric field of strength E, keeping the droplet stationary. Find an equation for the droplet's charge q, given the electric field E and the droplet's weight mg.

A tiny ink droplet of mass m_o and charge q moves horizontally through the air with a viscosity η. The ink droplet is propelled by an external electric field E but is constantly opposed by retarding force F_r = -6πηrv of the air. Determine an expression for radius r of the ink droplet such that it moves with terminal velocity v_t.

A pair of small, identical metallic balls are charged to +200 nC and -200 nC respectively. The balls are suspended in air by thin, non-conductive threads, as depicted in the accompanying diagram. An electric field of 500,000 N/C is applied as shown below. Determine the mass of each metallic ball.

In a lab, a researcher studies a "nano-diamond" with a permanent electric dipole moment of 5.0 x 10^-8 C•m. They place it 15 cm away from a minuscule charged metallic bead with a +10 nC charge aligned with the diamond's dipole axis. The goal is to calculate the electric force magnitude acting on the bead.

Two tiny spheres of charge, q_A = -30 nC, and q_B = +60 nC, are placed at the corners A and B of a right triangle (OAB), as shown in the figure. Determine the magnitude and direction of the net electric field generated at O by these two spheres.

Two tiny spheres of charge, q₁ = 2 μC and q₂ = 3 μC are separated by a distance of 31 cm and lie along the horizontal axis. The sphere with charge q₁ is on the left. Determine the electric field E vector at i) the midpoint between two charges and ii) 4 cm to the right of the charge q₂. 

A -16 nC tiny metallic sphere is placed at one corner of a square of side length 25 cm as shown in the image. Find the electric-field vector produced at the opposite corner of the square.

A metallic sphere of charge q and mass 1 kg is released from rest at a height d above a large plate. What magnitude and sign of charge would make the sphere suspended in the air? The electric field due to the plate is approximately 150 N/C and points toward the plate.

Two knights wearing metallic armor are 60 m apart on a charged road. They float in the air using the road's electric field that points downward and has a magnitude of 350 N/C. One of the knights is uniformly charged with a charge of -2 C and the other one is charged with a charge of -1.5 C. i) Find the force of repulsion (F) between the two knights. ii) Is it possible that one of the knights flies towards the other using the road's electric field?

A thin nonconducting disk, a nonconducting ring, and a tiny sphere carry (each of them) a charge of 130 nC uniformly distributed over their surfaces. Assume the charge on the disk is located on one face. The disk and the ring have the same radius of 10 cm. E_disk is the field produced at point X₁ located on the axis of the disk and at a distance of 30 cm from its center. E_ring is the field produced at point X₂ located on the axis of the ring and at a distance of 30 cm from its center. E_Sphere is the field produced at a point P₃ 30 cm away from the sphere. Compare E_disk , E_ring and E_sphere.

A sodium ion, Na⁺, is placed in space where the electric field is E = (-500i + 200k) N/C. Determine the electric force on the sodium ion. Express the force in terms of its components.

The helium atom consists of a spherical nucleus containing 2 protons. The nucleus is surrounded by 2 electrons orbiting around it at a distance of 1.0 × 10⁻¹² m. The radius of the helium nucleus is 1.6 × 10⁻¹⁵ m. Find the strength of the electric field generated by the nucleus at the electrons' orbit.

James is experimenting with a spherical Tesla coil in his garage. The coil has a diameter of 24 cm and is charged to 400,000 V. What is the electric field strength just outside the surface of the coil?

A fluorine ion with a negative charge of one electron is situated at the origin. Determine both the direction and strength of the electric field created by the fluorine ion at a point located 2.7 cm away from the ion.

A conducting spherical shell has an inner radius of 2.0 cm, an outer diameter of 3.8 cm, and a conductivity of 4.1 × 10 ^-7 Ω ^-1m ^-1. Determine the electric field at 2.8 cm from the center of the shell when a current of 3.2 A flows from the core to the shell's outer surface.

A particle with charge +3e and mass equal to that of an electron experiences an electric field strength equal to 1000 N/C. What will its resulting acceleration be, and how does it depend on electric field orientation? [elementary charge = 1.602 × 10⁻¹⁹ C, Mass of an electron = 9.11 × 10⁻³¹ kg]

Determine the magnitude and direction of an electric field in which an electron experiences a force of 3.36 × 10^-14 N towards the east.

An electron at a certain point in space experiences an acceleration of 3.6 million “g’s.” What is the electric field strength at that point?

Imagine a situation where four corners of a 50 cm by 50 cm square playground are occupied by charges. The playground has one corner with a charge of -30.0 μC and the other three corners with charges of -25.0 μC each. Calculate the electric field at the center of the square due to these charges.

A thin metal cord of length 3.00 m carries a total charge of 10.00 μC uniformly distributed along its length. What is the electric field at a point 1.5 cm perpendicular to the midpoint of the cord?

A proton is initially moving in the downward direction at a speed of 5.0 × 10⁶ m/s in an electric field. The electric field is uniform and is parallel to the direction of motion of the proton. For the proton to stop after traveling 6.0 cm, determine the strength required for the electric field and its direction.

A metal hoop of radius r has charge +q uniformly spread over it. Find out at what distance from the center along the axis, y = y_m, the magnitude of the electric field is maximum.

In a physics lab, two-point charges are placed along a straight line. Charge Q₁ has a magnitude of -25 μC, while charge Q₂ has a magnitude of 50 μC and is located 15 cm away from charge Q₁. As part of an experiment, you are tasked with finding the distance from Q₁ to the point where the electric field is zero.

Two unknown charges, Q₁ and Q₂, are placed far apart. At a point halfway between charges Q₁ and Q₂, the electric field is zero. What is the ratio of charge Q₁ to charge Q₂?

A uniformly charged ring with total charge -Q is shown in the figure below. It is centered at the origin with a radius R. A positive charge q is placed at the center. If q is displaced by a small distance y along the y-axis (perpendicular to the ring), i) find the expression for the spring constant that would result if the charge undergoes simple harmonic motion when released. ii) Then, determine the period of this motion if the mass of q is m.