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Find the electric field everywhere of an infinite uniform line charge with total charge Q.
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- A long cylinder of copper of radius 3 cm is charged so that it has a uniform charge per unit length on its surface of 3 C/m. (a) Find the electric field inside and outside the cylinder. (b) Draw electric field lines in a plane perpendicular to the rod.A charge of 30C is distributed uniformly a spherical volume of radius 10.0 cm. Determine the electric field due to this charge at a distance of (a) 2.0 cm, (b) 5.0 cm, and (c) 20.0 cm from the center of the sphere.Determine if approximate cylindrical symmetry holds for the following situations. State why or why not. (a) A 300-cm long copper rod of radius 1 cm is charged with +500 nC of charge and we seek electric field at a point 5 cm from the center of the rod. (b) A 10-cm long copper of radius 1 cm is charged with +500 nC of charge and we seek electric field at a point 5 cm from the center of the rod. (c) A 150-cm wooden rod is glued to a 150-cm plastic rod to make a 300 cm long rod, which is then painted with a charged paint so that one obtains a uniform charge density. The radius of each rod is 1 cm, and we seek an electric field at a point that is 4 cm from the center of the rod. (d) Same rod as (c), but we seek electric field at a point that is 500 cm from the center of the rod.
- Two parallel conducting plates, each of cross-sectional area 400 cm2, are 2.0 cm apart and uncharged. If 1.01012 electrons are transferred from one plate to the other, what are (a) the charge density on each plate? (b) The electric field between the plates?A point charge q=5.01012 C is placed at the center of a spherical conducting shell of inner radius 3.5 cm and outer radius 4.0 cm. The electric field just above the surface of the conductor is directed radially outward and has magnitude 8.0 N/C. (a) What is the charge density on the inner surface of the shell? (b) What is the charge density on the outer surface of the shell? (c) What is the net charge on the conductor?Consider a uranium nucleus to be sphere of radius R=7.41015 m with a charge of 92e distributed uniformly throughout its volume. (a) is the electric force exerted on an electron when it is 3.01015 m from the center of the nucleus? (b) What is the acceleration of the electron at this point?
- The circular are shown below carries a charge per unit length =0 cos . Where is measured from the x-axis. What is the electric field at the origin?Find the electric field everywhere of an infinite uniform line charge with total charge Q. Sol. Using Gauss's Law: PE - dÀ = EA = | E0 Since, its the line charge we use the area of a cylinder surrounding the line charge E*2T L= But all the charged get enclosed by the cylinder area, so denc = Q Deriving, we get: E = (1/2 TE0 )*( /rL)QUESTION 4 Find the electric field everywhere of an infinite uniform line charge with total charge Q. Sol. Using Gauss's Law: dA = %3D EA = Since, its the line charge we use the area of a cylinder surrounding the line charge E*2T L= But all the charged get enclosed by the cylinder area, so denc = Q Deriving, we get: E = (1/2 TTE0 )*( /rL)
- Find the electric field everywhere of an infinite uniform line charge with total charge Q. Sol. Using Gauss's Law: /EO EA = Eo Since, its the line charge we use the area of a cylinder surrounding the line charge E*2 L= But all the charged get enclosed by the cylinder area, so Cenc =Q Deriving we get: E= (1/2 TEO 1 IrL)Find the electric field everywhere of an infinite uniform line charge with total charge Q. Sol. Using Gauss's Law: DE - dÀ = EA = Since, its the line charge we use the area of a cylinder surrounding the line charge E*2T L= But all the charged get enclosed by the cylinder area, so denc = Q Deriving, we get: E= (1/2 TE0 )*( IrL)The electric field at a point in space is definedas the force per unit charge at that point inspace. We can write the electric field E ofa charge q at a distance d from that charge,experienced by a charge Q, asE =FQ= kqd2.The electric field has a direction such that itpoints toward negative charges and away frompositive charges. Suppose your rub a balloonin your hair and it acquires a static charge of−2 × 10−9 C.What is the magnitude of the electric fieldcreated by the balloon at a location 1 m duenorth of the balloon? Coulomb’s constant is9 × 109 N · m2/C2.Answer in units of N/C. You hair acquired an equal amount of positivecharge when you rubbed the balloon on yourhead.What is the strength of the electric fieldcreated by your head at the location of yourfeet, 1.5 meters below?Answer in units of N/C.