A wire is bent into a 90° circular arc of radius R and has a negative charge density of 2. (a) Draw a vector indicating the direction of the net electric field at point P. (b) Determine an integral expression in terms of one variable for the net electric field at point P and include the proper limits of integration. Do not evaluate the integral. R why? 2 R 90° P
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- 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 total charge 5.0106 C is distributed uniformly throughout a cubical volume whose edges are 8.0 cm long. (a) What is the charge density in the cube? (b) What is the electric flux through a cube with 12.0-cm edges that is concentric with the charge distribution? (c) Do the same calculation for cubes whose edges are 10.0 cm long and 5.0 cm long. (d) What is the electric flux through a spherical surface of radius 3.0 cm that is also concentric with the charge distribution?
- (b) Three pomt ciarges are located on a ciseular circumference of radius 3.0 cm as shown in Figure 2. At point P. om Fjure Draw the electric field exerted by each charge i. Find the electric field exerted by each charge m What are thie net electric field and its direction?.00 44E0 Give an expression for the electric field strength E at a point in terms of the charge q and distance r from the charge to that point. Use k for k = 47). Flag question (i.e. Use the following notation (without the quotes): "/" for division, "*" for multiplication, "+" an "-" as usual. For powers used "^2", while for square root use "sqrt". To indicate that square root applies to the whole expression use brackets - for example, for √AB use sqrt(A*B). For Greek letters such as π, a etc. use pi, alpha. For example to get 1 AVAB use 1/pi* A^2/B*sqrt(AB). Please use the exact variables given in the conditions of the problem: e.gif L is given, then do not use 1. Please use "Display response" button to check the you entered correct expression, before submitting your answer. л вOnd the total charge contained in cylindrical volume defined by r s 4m, and zs 5m if p, = 32rz² nC/m
- 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.Consider a thin plastic rod bent into an arc of radius Rand angle a (see figure below). The rod carries a uniformly distributed negative charge Q -Q A IR What are the components and E, of the electric field at the origin? Follow the standard four steps. (a) Use a diagram to explain how you will cut up the charged rod, and draw the AE contributed by a representative piece. (b) Express algebraically the contribution each piece makes to the and y components of the electric field. Be sure to show your integration variable and its origin on your drawing. (Use the following as necessary: Q, R, cx, 0, A0, and EQ-) ΔΕ, = - TE aR² AB=(2 Lower limit= 0 ✓ e aR² Upper limit= a X cos(0)40 x (c) Write the summation as an integral, and simplify the integral as much as possible. State explicitly the range of your integration variable. sin (0)40 x Evaluate the integral. (Use the following as necessary: Q, R, a, and E.) EditA charged sphere of radius Rohas charge density p=p,. Find the total charge in the sphere.
- Following the previous question, the x-component of the net electric field at x = -1.00 m, Enet.x , is N/C. Use normal format and 3 significant figures.The volume charge density of a spherically charged cloud changes with the distance to the cloud center as p(r) = po r a " where the parameters are po 1.85 nC/m³ and a = 22 m. Find the magnitude of electric field at distance d = 25 m from the cloud center. The electric field, E(r = 25 m) = 1484.65 Find the electric field (in N/C) as a function of r (in m). Do not submit the units. The electric field, E(r) = 1484.65 N/C. = Units N/CThree charged patides ar ocated at the comers of an equitateral triangle an shown in the figurn below (let a3.00 C, and 910 m). Calculate the total electric force on the 7,00-pc chargn. maituteA X N dron XCtercucwie from the