Home
Class 12
PHYSICS
The intensity of an electric field depen...

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

Text Solution

Verified by Experts

The correct Answer is:
`phi=4piRa, Q=4piRa in_(0)`
Promotional Banner

Topper's Solved these Questions

  • ELECTROSTATICS

    RESONANCE ENGLISH|Exercise Part - II|23 Videos

  • ELECTROMAGNETIC INDUCTION

    RESONANCE ENGLISH|Exercise A.l.P|19 Videos

  • EXPERIMENTAL PHYSICS

    RESONANCE ENGLISH|Exercise PART -II|10 Videos

Similar Questions

Explore conceptually related problems

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.

The intensity of an electric field depends only on the co-ordinates x, y and z as follows: vecE=a((xhati+yhatj+zhatk))/((x^2+y^2+z^2)^(3//2)) unit. The electrostatic energy stored between two imaginary concentric spherical shells of radii R and 2R with centre at origin is

A particle projected from origin moves in x-y plane with a velocity vecv=3hati+6xhatj , where hati" and "hatj are the unit vectors along x and y axis. Find the equation of path followed by the particle :-

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) .

If hati and hatj are unit vectors along X-and Y-axis respectively, then what is the magnitude and direction of hati +hatj and hati - hatj ?

The work done by the force = vec F = A (y^(2) hati + 2 x^(2) hatj) , where A is a constant and x and y are in meters around the path shown is.

If hati,hatj and hatk are unit vectors along X,Y & Z axis respectively, then what is the magnitude of hati + hatj + hatk

The electric field strength depends only on the x, y, and z coordinates according to the law E = (a(xhati+yhatj+zhatk))/(x^2+y^2+z^2)^3//2 , where a = 280 Nm^2C^(-1) is a constant. If the potential difference between (3,2,6) and (0,3,4) is x^2 . What is the value of x.

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.

The work done by the force vec(F)=A(y^(2) hati+2x^(2)hatj) , where A is a constant and x & y are in meters around the path shown is :

RESONANCE ENGLISH-ELECTROSTATICS-HLP
  1. A particle of charge -q and mass m moves in a circular orbit about a f...

    Text Solution

    |

  2. The field potentail in a certain region of space depends only on the...

    Text Solution

    |

  3. A conducting sphere S1 of radius r is attached to an insulating handle...

    Text Solution

    |

  4. The intensity of an electric field depends only on the coordinates x a...

    Text Solution

    |

  5. A solid non conducting sphere of radius R has a non-uniform charge dis...

    Text Solution

    |

  6. Two electric charges q and - 2 q are placed at a distance 6 m apart on...

    Text Solution

    |

  7. Two small metallic balls of radii R(1) & R(2) are kept in vacuum at a ...

    Text Solution

    |

  8. A ball of radius R carries a positive charges whose volume density at ...

    Text Solution

    |

  9. Consider an equilateral triangle ABC of side 2a in the plane of the pa...

    Text Solution

    |

  10. An electrostatic field line leaves at angle alpha from charge q(1) and...

    Text Solution

    |

  11. Figure shown two infinitely large conducting plates A and B. If electr...

    Text Solution

    |

  12. In a conducting hollow sphere of inner and outer radii 5 cm and 10 cm,...

    Text Solution

    |

  13. Figure shows a system of three concentric metal shells, A, B and C wit...

    Text Solution

    |

  14. A point charge q is brought slowly from infinity and is placed at the ...

    Text Solution

    |

  15. Consider two solid dielectric spheres of radius a, separated by a dist...

    Text Solution

    |

  16. A triangle is made from thin insulating rods of different lengths, and...

    Text Solution

    |

  17. A square of side d, made from a thin insulating plate, is uniformly ch...

    Text Solution

    |

  18. A point charge q is located between two mutually perpendicular conduct...

    Text Solution

    |

  19. A point charge q is located at a distance l from an infinite condutin...

    Text Solution

    |

  20. Four charges 2C, – 3C, –4C and 5C respectively are placed at all the ...

    Text Solution

    |