2. A uniform rod of length L lies on the x-axis as shown. The rod has a net charge of Q that is uniformly spread alongits length. P Q=+5.00e-9 C L=5.00 meters A uniformly charged rod of length L on the x-axis. Point P is at (5,2) meters on the x,y plane. Use the methods shown in class to: • Calculate the magnitude/size of the electric field at point P due to the rod. • Calculate the Trig Angle, measured counter-clockwise from the +x-axis in degrees, of the electric field at point P due to the rod.
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- 4) Consider a uniformly charged thin rod of length 3L and charge (+Q) lying along the x-axis as shown in the figure. Calculate the electric field at the point P a distance of L from the right end of the rod. y L 2L L +Q PThe electric field intensity 2m from the surface of a charged sphere is 30.86 x103 N/C. The charge densityat the surface of the sphere is 8.85 x 19‒7 coul/m2. What is the radius of the sphere ?• Hint: The Gaussian surface area of the big sphere of radius, r + 2 is : A = 4π (r +2 )2 Ans. r = 2.5 m•38 Figure 22-58a shows a circular disk that is uniformly charged. The central z axis is perpendicular to the disk face, with the origin at the disk. Figure 22-58b gives the magnitude of the electric field along that axis in terms of the maximum magnitude Em at the disk surface. The z axis scale is set by z, = 8.0 cm.What is the radius of the disk? Em ntre 0.5Em 2 z (cm) 8rm (a) (b)
- 2-3) Here's a classic problem. Consider two metal spheres of different radiuses RA and Rs, separated by a great distance. Sphere A has a charge Q and Sphere B is initially uncharged. Now suppose that we run a conducting wire from one to the other, then disconnect and discard the wire. A) Determine the amount of charge on each sphere in terms of the quantities given in the problem. B) Determine the magnitude of the electric field at the surface of each in terms of the quantities given in the problem. HINTS: There may be some information that was not discussed in class. First, the electric field at the surface of a metal is perpendicular to the surface of the metal. If it were not, there would be a component of E along the surface that would force charges to redistribute themselves until that component goes to zero. Second, once charges have stopped moving from A to B, what can you say about their surfaces? Lastly, you may want to consider Gauss's law.A satellite travels around Earth in uniform circular motion at an altitude of 35,736 km above Earth’s surface. The satellite is in geosynchronous orbit. In the below figure, the satellite moves counterclockwise (ABCDA). (State directions in terms of the x- and y-axes.) The radius of Earth is 6371 km. a.)What is the magnitude of the satellite’s average acceleration for one quarter of an orbit, starting at A and ending at B? b.)What is the direction of the satellite’s average acceleration for one quarter of an orbit, starting at A and ending at B? Enter the answer in degrees where negative indicates an angle below −x-axis and positive indicates an angle above −x-axis.PC-3 The figure to the right shows two source charges q₁ and 92 and a field point P on the x axis. a) Show at point P the direction and approximate relative magnitudes of: E₁ at P due to 1, E₂ at P due to q2, and Enet at P due to both q₁ and 92.3 b) Find the numerical value of the x and y components of Enet at P due to both q₁ and 92. y 3cm 3cm 191=-4µC 4cm 92 +7μC PC-3 P .X
- Problem 4: The electric field 1/7 of the way from a charge q1 to a charge q2 is zero. How many times larger is g2 than q, based on the previous statement? 92/91 =*•32 a0 In Fig. 22-50, positive charge q = 7.81 pC is spread uni- formly along a thin nonconducting rod of length L= 14.5 cm. What are the (a) magnitude and (b) di- rection (relative to the positive di- rection of the x axis) of the electric field produced at point P, at dis- tance R= 6.00 cm from the rod along its perpendicular bisector? -x L•30 o Figure 22-53 shows two concentric rings, of radii R and R' = 3.00R, that lie on the same plane. Point P lies on the central z axis, at distance D = 2.00R from the center of the rings. The smaller ring has uniformly distributed charge +Q. In terms of Q, what is the uni- formly distributed charge on the larger ring if the net electric field at Pis zero? R'
- •38 Figure 22-58a shows a circular disk that is uniformly charged. The central z axis is perpendicular to the disk face, with the origin at the disk. Figure 22-58b gives the magnitude of the electric field along that axis in terms of the maximum magnitude E, at the disk surface. The z axis scale is set by z, = 8.0 cm. What is the radius of the disk? En 0.5Em z (cm)1.) Write an expression for the magnitude of the electric field valid for r < R. 2.) Write an expression for the magnitude of the electric field valid for r>Rr>R.• A 12µC charge is placed at the origin,what is the electric field at x= 5.0m? If an electron is placed there what would be the electric force of the field.