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(a) consider an arbitrary electrostic fi...

(a) consider an arbitrary electrostic field configuration a small test charge is placed at a null point of the configuration show that the equailibrium of the test charge is necessarly unstable
(b) verify this result for the simple configuration of two charges of the same mangnitude and sign placed a certain distance apart

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(a) prove it by contradiction suppose the equlibrium is stable then the test charge displaed slighly in any direction will experience a retoring force towards the null point that is there is a net inward flux of electric field through a closed surface arougn the null point but gauss law the flux of electric field through a surface not enclosing any charge must be zero hence the equilibrium cannot be stable
(b) the mid point of the line joining the two charges is a null point displace a test charg from the null point slighly along the the line rememebr stability of equibrium needs restoring force in all direction
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(a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable. (b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

The method of electrical images is used to solve the electrostatic problems, where charge distribution is not specified completely. The method consists of replacement of given charge distribution by a simplified charge distribution or a signal point charge or a number of point charges [rovided the original boundary conditions are still satisfied. For example consider a system consider a system containing a point charge q placed at a distance d of form an infinite conducting plane. The boundary conditions are : (i) Potential is zero at infinity (ii) Potential is zero at each point on the conducting plane If we replaced the conducting plane by a point charge (-q) placed at a distance 'd' opposite to conducting plane. The charge (-q) is called the electrical image. Now system consists of two charge +q an -q at seperation 2d . If charge +q moves to a distance 'y' from the boundary of conducting plane (now absent), the electrical image -q also moves to the same 'y' from the boundary of conducting plane, so that the new distance between +q and -q is 2y The potential energy of system of charge +q placed at a distance d from the earthed conducting plane is

The method of electrical images is used to solve the electrostatic problems, where charge distribution is not specified completely. The method consists of replacement of given charge distribution by a simplified charge distribution or a signal point charge or a number of point charges [rovided the original boundary conditions are still satisfied. For example consider a system consider a system containing a point charge q placed at a distance d of form an infinite conducting plane. The boundary conditions are : (i) Potential is zero at infinity (ii) Potential is zero at each point on the conducting plane If we replaced the conducting plane by a point charge (-q) placed at a distance 'd' opposite to conducting plane. The charge (-q) is called the electrical image. Now system consists of two charge +q an -q at seperation 2d . If charge +q moves to a distance 'y' from the boundary of conducting plane (now absent), the electrical image -q also moves to the same 'y' from the boundary of conducting plane, so that the new distance between +q and -q is 2y The work done in carrying charge q from distance d to distance y from earthed conducting plane is

The method of electrical images is used to solve the electrostatic problems, where charge distribution is not specified completely. The method consists of replacement of given charge distribution by a simplified charge distribution or a signal point charge or a number of point charges [rovided the original boundary conditions are still satisfied. For example consider a system consider a system containing a point charge q placed at a distance d of form an infinite conducting plane. The boundary conditions are : (i) Potential is zero at infinity (ii) Potential is zero at each point on the conducting plane If we replaced the conducting plane by a point charge (-q) placed at a distance 'd' opposite to conducting plane. The charge (-q) is called the electrical image. Now system consists of two charge +q an -q at seperation 2d . If charge +q moves to a distance 'y' from the boundary of conducting plane (now absent), the electrical image -q also moves to the same 'y' from the boundary of conducting plane, so that the new distance between +q and -q is 2y The force between point charge +q and earthed conducting plane is

Answer carefully: (a) Two large conducting spheres carrying charges Q_(1) and Q_(2) are brought close to each other. Is the magnitude of electrostatic force between them exactly given by Q_(1),Q_(2)//4pi epsilon_(0)r^(2) , where r is the distance between their centres? (b) If Coulomb’s law involved 1//r^(3) dependence (instead of would Gauss’s law be still true ? (c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point? (d) What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical? (e) We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there? (f) What meaning would you give to the capacitance of a single conductor? (g) Guess a possible reason why water has a much greater dielectric constant (= 80) than say, mica (= 6).

Four charges Q_(1), Q_(2), Q_(3) and Q_(4) oof same magnitude are fixed along the x axis at x=-2a, -a, +a and +2a , respectively. A positive charge q is placed on the positive y axis at a distance b gt 0 . Four options of the signs of these charges are given in List I. The direction of the forces on the charge q is given in List II. Match List I with List II and select the correct answer using the code given below the lists. {:(,"List-I",,,"List-II"),((P),Q_(1)","Q_(2)","Q_(3)","Q_(4) "all positive",,(1),+x),((Q),Q_(1)","Q_(2) " positive, "Q_(3)","Q_(4)" negative",,(2),-x),((R),Q_(1)","Q_(4)" positive ,"Q_(2)","Q_(3)" negative",,(3),+y),((S),Q_(1)","Q_(3)" positive , "Q_(2)","Q_(4)" negative",,(4),-y):}

Two particles A and B having equal charges are placed at distance d apart. A third charged particle placed on the perpendicular bisector at a distance x will experience the maximum Coulomb’s force when :

Assetrion: If a proton and electron are placed in the same uniform electric field. They experience different acceleration Reason: Electric force on a test charge is independent of its mass

NCERT GUJARATI-ELECTRIC CHARGES AND FIELDS -EXERCISES
  1. Consider a uniform electric field E=3xx10^(3) hati N/C (a) what is ...

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  2. What is the net flux of the uniform electric field of exercise th...

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  3. Careful measurement of the electric field at the surface of a black b...

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  4. A point charge + mu c is a distance 5 cm directly above the centre of...

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  5. A point charge of 2.0 mu c is at the centre of a cubic gaussian ...

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  6. A point charge causes an elelctric flux of -1.0 xx10^(3) Nm^(2) /C to...

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  7. A conducting sphere of radius 10 cm has an unknown charge if the elect...

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  8. A uniformly charged conducting sphere of 2.4 m diameter has a (a)...

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  9. An infinite line charge produces a field of 9xx10^(4) N/C at a dis...

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  10. Two large thin metal plates are parallel and close to each other on...

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  11. An oil drop of 12 exess electrons is held stationary under a consta...

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  12. Which among the curves cannot possibly represent electrostatic fie...

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  13. In a certain region of space electric field is along the z direction...

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  14. (a) a conductor a with a cavity given a charge Q show that the enti...

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  15. A hollow charged conductor has a tiny hole cut in to its surface sho...

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  16. Obtain the formula for the electric field due to a long thin wire ...

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  17. It is now established that protons and neutrons are themselves bui...

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  18. (a) consider an arbitrary electrostic field configuration a small tes...

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  19. A particle of mass m and charge enters the region between the two char...

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  20. Suppose that the particle in exercise in 1.33 an electron projecrt...

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