1. In lecture, we derived the electric field a height z above the center of a...
1. In lecture, we derived the electric field a height z above the center of a thin ring of charge with constant charge per unit length λ. Let's assumie here that λ > 0. Suppose a negative point charge q with mass m s placed a very small distance above the center of the ring. Show that the point charge undergoes simple harmonic motion and find the frequency of small oscillations. Hint: show that near the center of the ring...
4. In lecture we derived the electric field a distance z above the center of a thin ring of charge and a uniform disk of charge. Now determine the electric field a distance z above the center of a ring with charge uniformly distributed between an inner radius Ri and an outer rads R2 (alternatively, you can describe this as a disk of rads 2 with a circular hole of radius R). Do this two ways: by directly performing an...
● În lecture we derived the electric field ǎ distance z above the center of thin ring of charge ad ă iniform disk of charge. Now determine the electric field a distance z above the center of a ring with charge uniformly distributed between an inner radius R1 and an outer radius R2 (alternatively, you can describe this as a disk of radius R2 with a circular hole of radius R1). Do this two ways: by directly performing an integral...
2 An infinite sheet of uniform surface charge density σ and an infinite sheet of uniform surface charge density parallel to each other and are separated a distance h as shown in the figure below: σ lie a) What is the electric field in regions A, B, and C? b) Suppose an electric dipole composed of a positive point charge +q and negative point charge -q both with mass m separated a distance d is placed in region B. If...
2. An infinite sheet of uniform surface charge density σ and an infinite sheet of uniform surface charge density-lie parallel to each other and are separated a distance h as shown in the figure below: +o a) What is the electric field in regions A, B, and C? b) Suppose an electric dipole composed of a positive point charge +q and negative point charge -q both with mass m separated a distance d is placed in region B. If the...
2. An infinite sheet of uniform surface charge density σ and an infinite sheet of uniform surface charge density parallel to each other and are separated a distance h as shown in the figure below: σ lie a) What is the electric field in regions A, B, and C? b) Suppose an electric dipole composed of a positive point charge +q and negative point charge -q both with mass m separated a distance d is placed in region B If...
2 An infinite sheet of uniform surface charge density σ and an infinite shi et of uniform surface charge density parallel to each other and are separated a distanceh as shown in the igure below σ lie to, -σ a) What is the electric field in regions A, B, and CY b) Suppose an electric dipole composed of a positive point charge and negative point charge -both with mass m separated a distance d is placed in region B. If...
3 points) An electron is constrained to move along the central axis of a ring of radius R which is uniformly charged with total positive charge Q (a) Show that if the electron is near the centre of the ring (a small distance compared to R), it will experience a force of the form Fz--kz (where z is the distance from the centre of ring) (b) Since this force will make the electron follow simple harmonic oscillation, derive a formula...
The electric field on the axis of a ring of charge near its center( which is located at z=0) is given by E(z)= ((kQ)/(R^3)) z. The ring has a radius R=5 and total charge of Q= 1 uC 1. A charged particle (m = 1 mg, q = –1 nC) is placed near the center of the ring. Write down and expression for the force F(z) that acts on the particle, in terms of kC, Q, q, R and z....
1. A cylinder of mass m, height h and radius r floats partially submerged in a liquid of density ρ. One third of the height of the cylinder is above the surface of the water. Johnny pushes the cylinder down by a small distance x<h/3, then he releases it from rest. A) prove that the resulting motion of the cylinder is a simple harmonic motion. B) Find the period of the small oscillations in terms of the given quantities (m,r,h,ρ)