Three straight wires (with one end at \(x = –L\) and the other end at \(x = +L\)) each have the same total charge \(+Q\) distributed differently. Wire A has charge density \(\lambda_A(x) = +\alpha x^2\text{.}\) Wire B has charge density \(\lambda_B(x) = +\beta \cos\left(\frac{\pi x}{2L}\right)\text{.}\) Wire C has uniform charge density \(+\lambda_C\text{.}\)
You want to predict how the electric fields of these three wires will compare a distance \(L\) above the center of each rod (along the \(y\)-axis). Rank the three wires by the magnitude of the electric field produced at this location from smallest to largest.
You have two point charges at different locations along the \(x\)-axis. Each charge can have either \(+q_o\) or \(-q_o\text{.}\) Sketch a charge diagram showing the configuration and sign of the charges if the electric field at the origin is zero.
A charged wire has one end at \(x = -L\) and the other end at \(x = L\text{.}\) The wire has a known, non-uniform charge density \(\lambda(x) = \frac{q_o}{L^2} x\text{.}\) You have an electric field generator that can make different electric fields, but when you set it to create a uniform electric field you find that the net force on the wire is 0! Which of the following alternate settings for your electric field generator would result in a nonzero net force on the wire?
A charged wire has one end at \(x = –L\) and the other end at \(x = L\text{.}\) The wire has a known, non-uniform charge density \(\lambda(x) = \frac{q_o}{L} \cos\left(\frac{\pi x}{2L}\right)\text{.}\) You have an electric field generator that can make the following three electric fields:
Which electric field will give you the smallest net force on the wire? Which will give you the largest net force on the wire? (You may calculate the net forces to check your answer, but your explanation should be qualitative.)
In the figure above, the charge on the left is \(+q_L\) and the total charge on the right is \(+q_R\text{.}\) The charges on the right are all identical and are spread out uniformly along an arc of radius \(R\text{.}\) Is the magnitude of the net electric force on \(+q_L\)greater than, less than, or equal to\(k\frac{q_L q_R}{R^2}\text{?}\)
In the figure below, the top charge has has a charge \(+q\text{,}\) and the two bottom charges have identical charge \(+Q\text{.}\) Determine the net electric force on the upper charge.
Find the electric field at the center of a square with charges of \(+q\text{,}\)\(+2q\text{,}\)\(+3q\text{,}\) and \(+4q\) on the corners (going clockwise starting from the upper right corner).
An electric dipole consists of two opposite charges \(\pm q\) separated by a small distance \(d\text{.}\) The product \(p=qd\) is called the dipole moment. The figure below shows an electric dipole perpendicular to an electric field \(\vec{E}\text{.}\) Determine an expression in terms of p and E for the magnitude of the torque that the electric field exerts on the dipole.
An electron is launched at a \(45^{\circ} \) angle and a speed of \(5.0×10^6\)\(m/s\) from the positive plate of the parallel-plate capacitor shown below. The electron lands \(4.0 \)\(cm\) away.
A positively charged wire with uniform charge density \(+\lambda\) lies along the \(x\)-axis and a negatively charged wire with uniform charge density \(-\lambda\) lies along the \(y\)-axis (both lines are infinitely long). Find the electric field at the point \((x, y)\text{.}\) You may look up the electric field due to an infinitely long wire with uniform charge density.
A straight wire with one end at \(x = –L\) and the other end at \(x = +L\) has a total charge \(+Q_o\) distributed uniformly along the right side and total charge \(-Q_o\) distributed uniformly along the left side. Find the electric field at a point on the \(y\)-axis a distance \(a\) from the center of the wire.
For each of the questions in the next activity, consider two charges placed at the locations shown in the image below (the circle is drawn for clarity -- it is imaginary). Let \(R = 5.0\) cm, \(q_1 = 3.0 \ \mu\)C, and \(q_2 = 1.0 \ \mu\)C. Now suppose that a proton is placed at the center of the circle.
Calculation21.8.13.Electric Field of Many Charges.
Consider a negative charge \(q_1\) = -9.00 nC that exists in a space far away from other charges. Let the charge \(q_1\) lie at the origin of a standard coordinate system. What is the electric field at a point P in space that has coordinates (2, -3, 6) m?
Determine the direction of the electric field at the center of the square in the figure, given that \(q_a\) = \(q_b\) = -1.00 \(\mu\)C and \(q_c\) = \(q_d\) = +1.00 \(\mu\)C.
