Home
Class 11
PHYSICS
In a certain region of space, the potent...

In a certain region of space, the potential is given by `V=k(2x^(2)-y^(2)+z^(2))`. The electric field at the point (1, 1, 1) has magnitude:

A

`k sqrt(6)`

B

`2k sqrt(6)`

C

`2k sqrt(3)`

D

`4k sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
`E=-((delV)/(delx)hati+(del V)/(del y)hatj+(delV)/(del z)hatk)=-k[4xhati-2yhatj+2zhatk]`
`=-k[sqrt(16+4+4)]=2k sqrt(6)`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS

    ALLEN |Exercise Exersice-03|7 Videos

  • MISCELLANEOUS

    ALLEN |Exercise ASSERTION-REASON|18 Videos

  • MISCELLANEOUS

    ALLEN |Exercise Part -II Example Some worked out Examples|1 Videos

  • KINEMATICS (MOTION ALONG A STRAIGHT LINE AND MOTION IN A PLANE)

    ALLEN |Exercise BEGINNER S BOX-7|8 Videos

  • PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT

    ALLEN |Exercise EXERCISE-IV|7 Videos

Similar Questions

Explore conceptually related problems

In a certain region of space, the gravitational field is given by -(k)/(r) where r is the distance and k is a constant. If the gravitaional potential at r=r_(0) be V_(0) , then what is the expression for the gravitaional potential (V)-

ln a certain region, the electric potential is given by the formula V (x, y, z) = 2x^(2)y + 3y^(3)z - 4z^(4)x . Find the components of electric field and the vector electric field at point (1, 1, 1) in this field.

In a certain region, the electric potential is given by the formula V(x ,y, z) = 6xy - y + 2yz Find the components of electric field and the vector electric field at point (1, 1, 0) in this field. Find the vector of electric at (1, 1, 0).

The potential energy (in joules ) function of a particle in a region of space is given as: U=(2x^(2)+3y^(2)+2z) Here x,y and z are in metres. Find the maginitude of x compenent of force ( in newton) acting on the particle at point P ( 1m, 2m, 3m).

If V=-5x+3y+sqrt(15)z then find magnitude of electric field at point (a, y, z).

The equation of an equipotential line in an electric field is y = 2 x , then electric field strength vectro at 1, 2 may be .

Potential energy function along x- axis in a certain force field is given as U(x)=(x^(4))/(4)-2x^(3)+(11)/(2)x^(2)-6x For the given force field :- (i)the points of equilibrium are x=1 , x=2 and x=3 (ii) the point x=2 is a point of unstable equilibrium. (iii) the points x=1 and x=3 are points of stable equilibrium. (iv) there exists no point of neutral equilibrium. The correct option is :-

A graph of the x-component of the electric field as a function of x in a region of space is shown in figure. The y- and z-components of the electric field are zero in this region. If the electric potential is 10 V at the origin, then the potential at x = 2.0 m is

Assum that an electric field vecE = 30 x^(2) hati exists in space. Then the potential difference V_(A) - V_(0) , where V_(0) the potential at the origin and V_(A) the potential at x = 2 m is :

In a uniform electric field, the potential is 10V at the origin of coordinates , and 8 V at each of the points (1, 0, 0), (0, 1, 0) and (0, 0, 1). The potential at the point (1, 1,1 ) will be .

ALLEN -MISCELLANEOUS-Exercise-01
  1. Uniform electric field of magnitude 100 V//m in space is directed alon...

    Text Solution

    |

  2. The equation of an equipotential line in an electric field is y = 2 x...

    Text Solution

    |

  3. In a certain region of space, the potential is given by V=k(2x^(2)-y^(...

    Text Solution

    |

  4. Figure shown two equipotential lies x, y plane for an electric field. ...

    Text Solution

    |

  5. The electric potential V(z, y,z) for a planar charge distribution is g...

    Text Solution

    |

  6. Three equal charges are placed at the corners of an equilateral triang...

    Text Solution

    |

  7. A non-conducting ring of radius 0.5 m carries a total charge 1.11xx10^...

    Text Solution

    |

  8. Two point charges +q and -q are held fixed at (-d,o) and (d,0) respect...

    Text Solution

    |

  9. The work in rotating electric dipole of dipole moment p in an electric...

    Text Solution

    |

  10. Which one of the following pattern of electric line of force can't pos...

    Text Solution

    |

  11. A sphere of radius R and charge Q is placed inside an imaginary sphere...

    Text Solution

    |

  12. Due to a charge inside a cube the electric field is E(x)=600 x^(1//2),...

    Text Solution

    |

  13. Electric flux through a surface of area 100 m^(2) lying in the plane i...

    Text Solution

    |

  14. Two spherical , nonconducting and very tin shells of uniformly distrib...

    Text Solution

    |

  15. A solid metallic sphere has a charge +3Q. Concentric with this sphere ...

    Text Solution

    |

  16. A hollow metal sphere of radius 5 cm is charged such that the potentia...

    Text Solution

    |

  17. A solid conducting sphere having a charge Q is surrounded by an unchar...

    Text Solution

    |

  18. A cube of a metal is given a positive charge Q. For the above system, ...

    Text Solution

    |

  19. A metallic solid is placed in a uniform electric field. The lines of f...

    Text Solution

    |

  20. A solid spherical conducting shell has inner radius a and outer radius...

    Text Solution

    |