10. Metal tube of infinite length and square cross-section with sides 0 ≤x≤L, 0 ≤ y ≤ L has three of its sides at potential zero and the fourth (y=L) in potential U. It is requested to determine the potential at inside the tube. Assume that along the contact lines of between surfaces with different potential there is a thin insulating material.
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- 2. The figure shows two parallel plates. The graph indicates the potential at points (X1= 0.300 m and X2= 0.400 m) between two plates, with V2 = 20 V and V1= 15 V. An electron is released from rest at x1, and that release point and the plate locations are aligned with the graph. What is the electrons speed (m/s) just as it runs into the plate? (You must decide which plate it hits) helpful info:: grap wo plate it hits.) V₂ V₁ 0 A | | X₁ X₂ e (Electron charge q = -1.6 x 10¹9 C, AK-q AV, electron mass = 9.1 x 10-³¹ kg, V=Joule/Coulomb, 1 eV = 1.6 x 10¹9 J, K-mv²/2)16, 17, 18The electric potential of a charged conducting sphere (as well as a spherical shell) can be calculated as Q R' V = k where is the charge and R is the radius of the sphere. Calculate the electric potential of a solid conducting sphere of a radius of R = 6 cm if the sphere loses 0.1% from the total number of its free electrons. The sphere is made of aluminum and has the density 2.7 g/cm³, molar mass 27 g/mol and one free electron per atom. Follow the steps listed below. 1. Find the number of free electrons per cm³ in aluminum. The number of free electrons per cm³, ne = Units Select an answer ✓ 2. Calculate the volume of the sphere and use it to find the total number of free electron inside the sphere. The number of free electrons, Ne = Units Select an answer 3. Calculate the charge of the sphere after it loses 0.1% of its electrons and use it to find the potential of the sphere. The electric potential of the sphere, V = Units Select an answer ✓
- Find the potential at points P₁, P2, P3, and P4 in the diagram due to the two given charges. PA 4 + +5 mC -4 cm Hint P₁ Figure Description a. Potential at P₁ = b. Potential at P₂ c. Potential at P3 = d. Potential at P₁ = = T 3 cm 2 cm- P31 -2 cm 3 cm 4 cm P2 V V V V 4 -10 MC (Yes, these numbers are quite large because even one millicoulomb is quite a large amount of charge. Use the "E" notation to enter your answers in scientific notation, if necessary, e.g. "3.14E12" for 3.14 × 10¹².)There is a non contuctive thin spherical shell with radius r=20 cm. It Carries a uniformly distributed + charge of q=1.5nC. The electric potential at point P, located at distance D=30cm from the sphere surface is equal to what? (The following have units V) a. 27 b. 45 c.54 d. 67 e. 150A charged conducting spherical shell of radius R = 3 m with total charge q = 23 μC produces the electric field given by E⃗ (r)={014πϵ0qr2r̂ forforr<Rr>R(PICTURE ATTACHED OF EQUATION) a. Enter an expression for the electric potential inside the sphere ( r < R ) in terms of the given quantities, assuming the potential is zero at infinity. V(r)= b. Calculate the electric potential, in volts, at radius r inside the charged shell. V(r) =
- 5. A 4.0-nm-diameter protein is in a 0.05 M KCl solution at 25°C. The protein has 9 positive and 20 negative charges. Model the protein as a sphere with a uniform surface charge density. What is the electric potential of the protein (a) at the surface and (b) 2.0 nm from the surface?1. A ball of solid conductor is given an electric charge so that the magnitude of the electric potential just outside the ball is 100 V, while the electric potential at a distance of 10 cm outside the surface of the ball is 20 V. Determine the radius of the conducting ball and the electric potential at a distance of 20 cm outside the ball.4. An aluminum sphere is placed in a previously uniform electric field. Find the electric potential after the sphere has been added. (Hint: this problem is artificial in that we assume that the electric field at infinity is E 2). What is the potential for a constant field? 1 E,ż urite down boundary unditens t02=-7V R A,+r +P V = 0 vire)= then ure E (Arre + Be t. re) Pelloso)
- 8. Figure below shows a ring of outer radius R = 13.0 cm and inner radius l'inner = 0.200R. It has uniform surface charge density 0 = 6.20 pC/m². With V = 0 at infinity, find the electric potential at point P on the central axis of the ring, at distance z = 2.00R from the center of the ring. 6 dQ K √ ₁7 - Pl What is your dQ? What is your infinitesimal area element? (a) Start with the formula for the potential: V = k What are your vectors r and r'? What is the distance to point P? What is dV? Potential due to a small ring of charge on the disk? (b) Write out the integral that you need to compute to get V. What are the bounds? (c) Once you get an expression for V, solve numerically. (d) Check to see if the units of your expression makes sense for V.Q1. What is the electric potential of a dipole on the y-axis at large distances? 1 qd 1 qd (c) V = 2nɛ, r? 1 qd 4πε r (a) V = 0 (b) V = (d) V = 2πε, r y Q2. Find the monopole term in the multi-pole expansion of the electric potential on the z- axis for a flat circular charged disk of radius R and charge density o (r,q) = krʻ cosʻ q, where k is a constant and r, q are polar coordinates with the origin at the disk's centre.1. Find the electric potential at a distance r from the center o of a spherical shell of radius R with charge Q distributed uniformly on the surface of the shell. Consider both cases: r R. Q R