25. Electric Potential

A total charge Q is uniformly distributed on a thread of length ℓ. The thread forms a semicircle. What is the potential at the full-circle’s center? (Assume V = 0 at large distances.)

Calculate the electric potential due to a tiny dipole whose dipole moment is 4.8 x 10⁻³⁰ Cm at a point 4.1 x 10⁻⁹ m away if this point is along the axis of the dipole nearer the positive charge.

Calculate the electric potential due to a tiny dipole whose dipole moment is 4.8 x 10⁻³⁰ Cm at a point 4.1 x 10⁻⁹ m away if this point is 45° above the axis but nearer the positive charge.

An analog voltage signal can vary from 0 V to 5.00 V, and it is to be converted to an 8-bit binary representation. What voltage, to the nearest 0.01 V, would have a binary representation of 01110101?

An analog voltage signal can vary from 0 V to 5.00 V, and it is to be converted to an 8-bit binary representation. What binary number would best represent 3.47 volts?

A lightning flash transfers 4.0 C of charge and 5.2 MJ of energy to the Earth. Across what potential difference did it travel?

A thin rod of length 2ℓ is centered on the x axis as shown in Fig. 23–46. The rod carries a uniformly distributed charge Q. Determine the potential V as a function of y for points along the y axis. Let V = 0 at infinity.

The wire in FIGURE P25.74 has linear charge density λ. What is the electric potential at the center of the semicircle?

A hollow cylindrical shell of length L and radius R has charge Q uniformly distributed along its length. What is the electric potential at the center of the cylinder?

Consider a uniformly charged sphere of radius R and total charge Q. The electric field E_out outside the sphere (r≥R) is simply that of a point charge Q. In Chapter 24, we used Gauss’s law to find that the electric field E_in inside the sphere (r≤R) is radially outward with field strength $Ein=\frac{1}{4\pi {ϵ}_0}\frac{Q}{R^3}r$. What is the ratio V_center/V_surface?

In the Bohr model of the hydrogen atom, an electron orbits a proton (the nucleus) in a circular orbit of radius 0.53 x 10^-10 m. What is the electric potential at the electron’s orbit due to the proton?

(II) In the commonly used “ASCII” code, numbers, letters and other symbols are stored as 8-digit binary numbers. The code for the letter A is 00100001, and the next letters are just the next binary numbers.

(a) What binary numbers are used to store C and T?

(II) In the commonly used “ASCII” code, numbers, letters and other symbols are stored as 8-digit binary numbers. The code for the letter A is 00100001, and the next letters are just the next binary numbers. What would be the decimal numbers for ASCII B and H?

A uniform electric field $\vec{E}=-6.30\text{N/C}\hat{i}$ points in the negative x direction as shown in Fig. 23–40. The x and y coordinates of points A, B, and C are given on the diagram (in meters). Determine the differences in potential V_BA.

A uniform electric field $\vec{E}=-6.30\text{N/C}\hat{i}$ points in the negative x direction as shown in Fig. 23–40. The x and y coordinates of points A, B, and C are given on the diagram (in meters). Determine the differences in potential V_CB.