Home
Class 11
PHYSICS
The energy density u is plotted against ...

The energy density u is plotted against the distance r from the centre of a spherical charge distribution on a log-log scale. Find the magnitude of slope of obtained straight line.

Text Solution

Verified by Experts

The correct Answer is:
4
`u=1/2 in_(0) E^(2)=1/2 in_(0)(q/(4pi in_(0) r^(2)))^(2)=q^(2)/(32 pi^(2) in_(0) r^(4))rArr log u= log (q^(2)/(32 pi^(2) in_(0) r^(4)))=log k-4 log r`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS

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

  • MISCELLANEOUS

    ALLEN|Exercise Exercise-01|87 Videos

  • MISCELLANEOUS

    ALLEN|Exercise SUBJECTIVE QUESTION|9 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|8 Videos

Similar Questions

Explore conceptually related problems

If the law of gravitation be such that the force of attraction between two particles vary inversely as the 5//2^(th) powr of their separation then the graph of orbital velocity v_(0) plotted against the distance r of a satellite from the earth's centre on a log-log scale is shown alongside the slope oline will be

A solid sphere of radius R has total charge Q. The charge is distributed in spherically symmetric manner in the sphere. The charge density is zero at the centre and increases linearly with distance from the centre. (a) Find the charge density at distance r from the centre of the sphere. (b) Find the magnitude of electric field at a point ‘P’ inside the sphere at distance r_1 from the centre.

For spherical charge distribution gives as . {{:(,rho = rho_(0)(1-(r)/(3)),"when" r le 3m),(,rho = 0 ,"when" r gt 3m):} ( where x is the distance form the centre of spherical charge distribution) The electric field intensity is maximum for the value of r=_______m.

A sphere of radius R carries charge such that its volume charge density is proportional to the square of the distance from the centre. What is the ratio of the magnitude of the electric field at a distance 2 R from the centre to the magnitude of the electric field at a distance of R//2 from the centre?

Figure shows a point charge +Q, located at a distance R/2 from the centre of a spherical metal shell. Draw the electric field lines for the given system.

A particles moves along a circle of a fixed radius with a variable acceleration given by a_(n) = kt^(n), where k is a constant and t time. If the power 'P' delivered by all forces acting on it be plotted against time 't' on a log-log scale, the slope of the straight line obtained is 2 as shown in Figure below. The value of n is:

For a spherically symmetrical charge distribution electric field at a distance r from the centre of sphere is vec(E)=kr^(2)hat(r) where k is a constant what will be the volume charge density at a distance r from the centre of sphere?

The correct plot of the magnitude of magnetic field vecB vs distance r from centre of the wire is, if the radius of wire is R

The gravitational potential energy of a body at a distance r from the centre of earth is U . Its weight at a distance 2r from the centre of earth is

ALLEN-MISCELLANEOUS-Part -II Example
  1. Two positrons (e+) and two protons (p) are kept on four corners of a s...

    Text Solution

    |

  2. Four charges are placed at the circumference of a dial clock as shown ...

    Text Solution

    |

  3. A small electric dipole is placed at origin with its dipole moment dir...

    Text Solution

    |

  4. Uniform electric field of magnitude 100 V//m in space is directed alon...

    Text Solution

    |

  5. Figure shows a uniformly charged hemisphere of radius R. It has a volu...

    Text Solution

    |

  6. A metallic rod of length I rotates at angular velocity omega about an...

    Text Solution

    |

  7. Consider a finite charged rod. Electric field at point P (shown) makes...

    Text Solution

    |

  8. The alectric potential in a region is given by the relation V(x)=4+5x^...

    Text Solution

    |

  9. A thin homogeneous rod of mass m and length l is free to rotate in ver...

    Text Solution

    |

  10. A thin homogeneous rod of mass m and length l is free to rotate in ver...

    Text Solution

    |

  11. A thin homogeneous rod of mass m and length l is free to rotate in ver...

    Text Solution

    |

  12. A simple pendulum is suspended in a lift which is going up with an acc...

    Text Solution

    |

  13. The variation of potential with distance x from a fixed point is shown...

    Text Solution

    |

  14. The energy density u is plotted against the distance r from the centre...

    Text Solution

    |

  15. The figure shown four situations in which charges as indicated (q gt 0...

    Text Solution

    |

  16. An electric field is given by vec(E)=(yhat(i)+xhat(j))N/C. Find the wo...

    Text Solution

    |

  17. The arrangement shown consists of three elements. (i) A thin rod of ...

    Text Solution

    |

  18. Six charges are kept at the vertices of a regular hexagon as shown in ...

    Text Solution

    |

  19. Electric field in a region is given by vec(E)=-4xhat(i)+6yhat(j). The ...

    Text Solution

    |

  20. An infinite plane of charge with sigma=2 in(0) C/m^(2) is tilted at a ...

    Text Solution

    |