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1. There are 7 particles arranged as shown in the gure. The side length of the square is 0.04m. How much work is required to carry a +6e charge from infinitely far to the midpoint of the square? )I 2e _e .- -38 +23 I. x +33 +9 +33 2. A researcher is conducting an experiment on electric potential, where he is trying to make X number of electrons form a certain pattern. In the rst pattern, these electrons are placed uniformly in a small ring with a circular electron arrangement pattern and the distance between the electrons is equal to each other. In the second pattern, similar to the rst one, only one electron is taken and placed in the center of the ring. Calculate the minimum value of X so that this second pattern has less energy than the rst pattern. 3. A sphere of radius R has a charge Q which is evenly distributed throughout the sphere. If at innity the value of the electric potential V is zero, (a) what is the value of V inside the sphere? (b) what is the potential difference between the point on the surface of the sphere and the point at the center of the sphere? 4. A proton is at rest and in a xed position. An electron is red at a proton with an initial velocity of 0.32 Mm/s. If initially the electron is very far om the proton, how far will the electronproton be so that the instantaneous velocity of the electron is double the initial velocity?| 5. An electron is initially at rest on the surface of a spherical conductor with a radius of 0.01 m and charge of 1.6 m0 coulombs. What is the initial velocity required for this electron to escape from this conducting sphere to an innity far point and zero kinetic energy there