O l6 charges ave fositioned as Shown below, each carryina a magnitude of Charge Q. Rank the baussian Surfaces according to the magnitude of SE dA, gveatest first. Note: EtdA ave vectors. A) a,d,c,b BJ a, b, d, C C)d, a,c, b Dd, b,a,c
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- The charge per unit length on the thin rod shown below is . What is the electric field at the point P? (Hint: Solve this problem by first considering the electric field dE at P due to a small segment dx of the rod, which contains charge dq=dx . Then find the net field by integrating dE over the length of the rod.)Positive charge is distributed with a uniform density along the positive x-axis from r to , along the positive y-axis from r to , and along a 90( arc of a circle of radius r, as shown below. What is the electric field at O?Suppose that the charge density of the spherical chargedistribution shown in Figure 6.23 is p(r)=p0r/R for rR and zero for rR . Obtain expressions for theelectric field both inside and outside the distribution.
- Shown below ale two concentric conducting spherical shells of radii R1 and R2 , each of finite thickness much less than either radius. The inner and outer shell carry net charges q1 and q2 , respectively, where both q1 and q2 are positive. What is the electric field for (a) rR1 ; (b) R1rR2 , and (c) rR2 ? (d) What is the net charge on the inner surface of the inner shell, the outer surface of the inner shell, the inner surface of the outer shell, and the outer surface of the outer shell?A sphere of radius R has a charge distribution given by rho(r)=A√r where A is a constant. What is the divergence of the electric field at the point r=R/2? Hint: What is the differential form of Gauss’ law?Charge is distributed uniformly with a density p throughout an infinitely long cylindrical volume of radius R. Show that the field of this charge distribution is directed radially with respect to the cylinder and that E=pr20 (rR); E=pR220r (rR).
- 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?A total charge Q is distributed uniformly throughout a spherical volume that is centered at o1 and has a radius R. Without disturbing the charge remaining charge is removed from the spherical volume that is centered at o2 (see below). Show that the electric field everywhere in the empty region is given by E=Qr40R3 where r is the displacement vector directed from o1 to o2 .A particle of charge q and mass m is placed at the center of a uniformly charged ring of total charge Q and radius R. The particle is displaced a small distance along the axis perpendicular to the plane of the ring and released. Assuming that the particle is constrained to move along the axis, show that the particle oscillates in simple harmonic motion with a frequency f=12qQ40mR3.
- Four charged particles are positioned at the corners of parallelogram as shown below. If q=5.0C and Q=8.0C , What is the net force on q?The electric field in a particular thundercloud is 2.0105N/C . What is the acceleration of an electron in this field?A spherical water droplet of radius 25 m carries an excess 250 electrons. What vertical electric field is needed to balance the gravitational force on the droplet at the surface of the earth?