Home
Class 12
PHYSICS
Determine the electric field strength ve...

Determine the electric field strength vector if the potential of this field depends on x, coordinates as
(a) `V = a (x^2 — y^2)` (b) `V = axy`
where, a is a constant.

Text Solution

Verified by Experts

`E_(x) =(delV)/(delx) = -2Ax and E_(y) = -(delV)/(dely)=2Ay`
`barE=E_(x) hati +E_(y) hatj = 2A (-x hati +yhatj)`
Promotional Banner

Topper's Solved these Questions

  • ELECTRIC FIELD AND POTENTIAL

    AAKASH SERIES|Exercise EXERCISE (LONG ANSWER QUESTIONS)|3 Videos
  • ELECTRIC FIELD AND POTENTIAL

    AAKASH SERIES|Exercise EXERCISE (SHORT ANSWER QUESTIONS)|6 Videos
  • ELECTRIC CHARGES AND FIELDS

    AAKASH SERIES|Exercise Practice Exercise|57 Videos
  • ELECTROMAGNETIC INDUCTION

    AAKASH SERIES|Exercise Additional Exercise|11 Videos

Similar Questions

Explore conceptually related problems

Determine the electric field strength vector if the potential of this field depends on X, coordinates as V = 10 axy

Determine the electric field strength vector if the potential of this field depends upon x - and y - coordinates as : (i) V = a(x^2 - y^2) (ii) V = a x y .

A partical of mass m is located in a unidimensionnal potential field where potentical energy of the partical depends on the coordinates x as U (x) = (A)/(x^(2)) - (B)/(x) where A and B are positive constant. Find the time period of small oscillation that the partical perform about equilibrium possition.

The electric field and the electric potential at a point are E and V respectively.

Find the potential function V (x,y) of an electrostatic field vec(E)=2axy hat(i)+a(x^(2)-y^(2))hat(j) where a is a constant.

Find the potential V of an electrostatic field vec E = a(y hat i + x hat j) , where a is a constant.

The field potentail in a certain region of space depends only on the x coordinate as varphi = -ax^(2) + b , where a and b are constants. Find the distribution of the space charge rho (x) .

The intensity of an electric field depends only on the coordinates x and y as follows, E = (a(xhati +y hatj))/(x^(2)+y^(2)) where, a is constant and hati and hatj are the unit vectors of the x and y axes. Find the charges within a sphere of radius R with the centre at the origin.

Gravitational potential in x-y plan varies with x and y coordinates as V = x^(2)y+2xy Find gravitational field strength E .

If the potential function is define as V = ( - 3 x + 4y + 12 z)V , then magnitude of electric field E( x,y,z) is

AAKASH SERIES-ELECTRIC FIELD AND POTENTIAL-PROBLEMS (LEVEL-II)
  1. Determine the electric field strength vector if the potential of this ...

    Text Solution

    |

  2. A metal sphere with its centre at A and radius R has a charge 2q on it...

    Text Solution

    |

  3. Two similar metal spheres are suspended by silk threads from the same ...

    Text Solution

    |

  4. A body of mass 2 gm is projected horizontally from the top of tower of...

    Text Solution

    |

  5. A body of mass 10 gm and having charge 2C is attached to a spring whic...

    Text Solution

    |

  6. Four charges Q, q, Q and q are placed at the corners A, B, C and D of ...

    Text Solution

    |

  7. A charge Q is fixed on the X-Y plane at point (0, a). Find the electri...

    Text Solution

    |

  8. Two charges 4q and q are fixed at points (0,9) and (12, 0) respectivel...

    Text Solution

    |

  9. Four point charges +q,+q,-q and -q are placed on the corners of a squa...

    Text Solution

    |

  10. Two point charges 4muC and 9muC are separated by 50 cm. The potential ...

    Text Solution

    |

  11. Two insulating plates are uniformly charged in such a way that the pot...

    Text Solution

    |

  12. A field of 100Vm^(-1) is directed at 30° to positive x-axis. Find (VA...

    Text Solution

    |

  13. A hollow sphere of radius 2R is charged to V volts and another smalle...

    Text Solution

    |

  14. Two identical particles of mass m carry a charge Q each. Initially one...

    Text Solution

    |

  15. Two dipoles that are back to back form a linear quadrapole i)...

    Text Solution

    |

  16. Two particles of mass m and 2m with charges 2q and q are placed in a u...

    Text Solution

    |

  17. A cone made of insulating material has a total charge Q spread uniform...

    Text Solution

    |

  18. Electrical potential .v. in space as a function of co-ordinates is giv...

    Text Solution

    |

  19. A solid dielectric (K = 1) sphere of radius R is charged uniformly by ...

    Text Solution

    |

  20. A uniform rod of length l and mass m is given a charge Q and is suspen...

    Text Solution

    |

  21. A rod of length L has a total charge Q distributed uniformly along its...

    Text Solution

    |