Over a certain region of space, the electric potential is V(x,y,z) = 10 x - 6xy +4yz2. The z-component of the electric field E, is a) E, =-(8yz) N/C b) E, = (-10 + 6y) N/C c) E, = (6x - 4z2) N/C d) E, = (-10 +6x2- 4z2) N/C e) E, = (-10 + 6x - 4z2) N/C. %3D
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- Over a certain region of space, the electric potential is V = 4x – 2x²y + 7yz?. (a) Find the expressions for the x, y, z components of the electric field over this region. (Use any variable or symbol stated above as necessary.) Ex Ey Ez (b) What is the magnitude of the field at the point P that has coordinates (1.00, 0, -7.00) m? N/CProblem 18: The electric potential in a certain region is given by the equation V(x,y,z) = 3αx2y3 - 2γx2y4z2 where the potential is in volts when the positions are given in meters. Part (d) The constants in this equation are α = 5.2 V/m5 and γ = 1.39 V/m8. Using this information, calculate the magnitude of the electric field at the point (x1,y1,z1) = (-5.0, 2.0, 1.5) m in units of newtons per coulomb.In a certain region of space, the electric potential is V(1, y, z) = Bzy – Cy² + Az where A, B and C are positive constants. Calculate the r, y and z components of the electric field. E, = -Cy+ 2Ar , Ey= -Cx – B , E,=0 %3D E = -3Cz + 2 Ar , E, = 0, E, = -3Cx-B %3D %3D E, = -Az + 2Br , E, = 0 , E, = - Ax – C
- A uniform electric field pointing in positive x direction exists in a region. Let A be the origin, B be the point on the x-axis at x =1 cm and C be the point on the y-axis at y =+1 cm. Then the potentials at the points A, B and C satisfy: (a) VA VB (ce) VASV (d) V> VcAn electric field Ë = A(3x²y°z*i +2x°yz² j+2x°y°zk ) exists in space. Ifelectric potential at (2, 2, 2) is taken to be zero then potential at point (1, 2, 2) is (b) 64A (a) 128A (c) 32A (d) 112AIn a certain region R of space, the electric potential is given by: V=x-y+xy+2z (V). Find the electrostatic energy stored in a cube of sides 1-2 m, centered on the origin of coordinates. a) 0,136 nJ b) 0,236 nJ c) 0,336 nJ d) 0,436 nJ e) 0,536 nJThe electric potential is given by V(r, y, 2) = Ar"y²z where A is a constant. Find the electric potential (where i, 3, and k are the unit vectors corresponding to z, y, and z axes in the three dimensional Cartesian Coordinate System). Select one: O -Ar'y=(i+ j + k) -3Az?y²zi = 2Ar*yzj – Ar"y?k -Aryzi – Ar'yzj – Ar*y?k O 3Ar²y²zi+2Ar*yzj+ Ar®y?k - Ar'y?z(3i + 2j + k)For a spherical surface with radius 0.15 m and is charged by 29 nC, the electric Potential V at r = 0.26 m is (in V)Consider an electric potential as a function of the distance r, 1 2A V(r) = (1 - ²/ ((₁-²4) (₁ + ¹24² ) - 1). 2 What happens to the electric field at r = 6A? OA. E>0 OB. E<0 OC. E=0 OD. Ē→ ∞Recommended textbooks for youCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University PressPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio…PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSONCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University PressPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio…PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON