An electric dipole with dipole moment P = (3.04î + 4.32 )(1.40 × 10 30 C-m) is in an electric field É = (4000 N/C)î. (a) What is the potential energy of the electric dipole? (b) What is the magnitude of torque acting on it? (c) If an external agent turns the dipole %3D until its electric dipole moment is P = (-4.32 i + 3.04)(1.40 × 10 30 C-m), how much work is done by the agent?

Liquid water has a large dielectric constant of ɛ, = 80. Suppose that a single sodium ion (Na+, carrying a positive charge of +1e) is held in the middle of a beaker of pure water. Compared to the volume of the sodium ion, the volume of the water can be effectively treated as infinite. a) Write down the electric displacement at r distance away from the sodium ion. b) Write down the electric field at r distance away from the sodium ion. c) Write down the electrostatic force that the sodium ion acts on a water molecule that is 2nm away from the ion and oriented with its dipole moment radially away from the ion. d) Calculate the polarization at a distance r = 2nm away from the sodium ion. e) The dipole moment of a water molecule is 6.17 x 10-30C · m. Estimate how much fraction of the water molecules that are at 2nm away from the sodium ion are reoriented by the sodium ion. (Assume that there are only two possible states for these water molecules: either randomly oriented and showing zero…

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An electric dipole consists of charges +2e and -2e separated by 1.1 nm. It is in an electric field of strength 3.1 × 106 N/C. Calculate the magnitude of the torque on the dipole when the dipole moment is (a) parallel to, (b) perpendicular to, and (c) antiparallel to the electric field. (a) Number i Units (b) Number i Units (c) Number i Units

Consider a polar molecule such as water, which has an electrical dipole moment of 6×10-30 Cm. Suppose we place such a molecule in an external electric field of 3.5×10-6 N/C. What is the difference in potential energy between the dipole moment being parallel to and anti-parallel to the electric field?

The membrane surrounding a living cell consists of an inner and an outer wall that are separated by a small space. Assume that the membrane acts like a parallel plate capacitor in which the effective charge density on the inner and outer walls has a magnitude of 6.8 × 10-6 C/m2. (a) What is the magnitude of the electric field within the cell membrane? (b) Find the magnitude of the electric force that would be exerted on a potassium ion (K+; charge = +e) placed inside the membrane.

A spherical capacitor is composed of two concentric conducting spheres, one of radius a and the other of radius c (c > a). In addition, between the two conductors there is a spherical shell of dielectric material (relative permittivity/relative dielectric constant ) with inner radius b (c > b > a) and outer radius c. The charge on the inner conductor is +Q. The charge on the outer conductor is -Q. (a) Make a sketch of the situation, indicating the relevant dimensions. (b) Determine the magnitude of the electric field E at radius r for a < r < b. (c) Determine the magnitude of the electric field E at radius r for b < r < c. (d) What is the (induced) surface charge density on the inner surface of the dielectric. (e) Sketch the radial component of the electric field versus r . (f) Sketch the electrostatic potential versus r . (g)Calculate the potential difference between the conductor at r = a and that at r = c. (h) What is the capacitance of this capacitor?

An electric dipole with dipole moment 4×10−9 Cm is aligned at 30° with the direction of a uniform electric field of magnitude 5×104 NC−1. Calculate the magnitude of the torque acting on the dipole.

I need help for these questions, I am studying for the physics exam and I couldn't solve this questions which are in the study plan of physics-102. Thanks in advance.