Electric charges and fields

 

Electric Charges and Fields

  
 Problems

Question1. Two free protons and two free electrons are separated by the same distance. Compare coulomb’s forces of repulsion between the pair of protons and pair of electrons.

Solution. The forces are the same because each proton carries a charge of the same magnitude as each electron and the distance between them is the same.

Question2. A charge Q is kept in the inner cavity and a charge 2Q is given to the inner shell. A charge 3Q is given to the outermost shell, as shown in the given figure. Find the charges at the surfaces A, B, and C.

Solution. Due to induction, -Q charge is induced on the inner surface A of the inner shell and +Q charge is induced on the outer surface B of the outer shell. Thus charge on the surface A= -Q.                                                                                                                         

 Now charge on surface B = 2Q + Q = 3Q 

Due to induction, - 3Q charge is induced on the inner surface of the outer shell and + 3Q charge is induced on the outer surface of the outer shell. Thus, total charge on the surface C = 3Q + 3Q = 6Q.

Question3. A negatively charged ebonite rod attracts a suspended ball of straw. Can we infer that the ball is positively charged?

Solution. No, because the negatively charged rod can attract an uncharged ball to induction and can also attract a positively charged ball, due to the Coulomb force of attraction.

Question4. Can two similar charged balls attract each other?

Solution. Yes, when the charge on one, say A is much larger than the charge on the other, say B. On account of induction, the ball B carrying a smaller charge shall acquire some net charge of opposite sign lying closer to A. Hence B will experience some net force of attraction.

Question5. A glass rod rubbing with silk is brought close to two uncharged metallic spheres in contact with each other, inducing charges on them as shown in the given figure. Describe what happens when

(1) The spheres are slightly separated.

(2) The glass rod is subsequently removed and finally.

(3) The spheres are separated far apart.

Solution. A glass rubbed with silk acquires a positive charge. When this rod is brought close to two uncharged metallic spheres A and B in contact, negative charge is induced on the left side of sphere A and an equal positive charge is induced on the right side of sphere B.

(1) When the spheres are slightly separated, the induced charges are shown in the above figure.

(2) As the glass rod is removed subsequently and separation is too small, the distribution of charges on A and B remains the same as shown in the  figure.

(3) When A and B are placed at a larger distance, the positive charges and negative charges on each flow and neutralize so that no charges in left on A and B.

Question6. Give reasons.

(a) A comb run through one's hair attracts small bits of paper. Why? What happens if the hairs are wet or if it is a rainy day? 

(b) Ordinary rubber is an insulator. But the special rubber tires of air craft’s are made slightly conducting. Why is this necessary?

(c) Vehicles carrying inflammable materials usually have metallic ropes touching the ground during motion. Why?

 (d) A bird perches on a bare high power line, and nothing happens to the bird. A man standing on the ground touches the same line and gets a fatal shock. Why?

Solution. (a) This is because the comb gets charged by friction. If the hair-are wet, or if its a rainy day, friction between the hair and the comb reduces. The comb does not get charged, and it will not attract small bits of paper.

 (b) The special rubber tyres of air craft’s are made slightly conducting so that electricity generated on account of friction between the tyres and the runway goes to earth.

 (c) When a vehicle moves, its body gets charged on account of friction due to air. The tyres also accumulate the charge on account of friction between the tyres and the road. The metallic ropes from the vehicle touching the ground enable the accumulated charges to flow to earth. This would otherwise be hazardous to the inflammable materials.

 (d) When a bird perches on a single bare high power line, nothing happens to him as no current flows through his body because the circuit is not completed. In the case of a person standing on the ground, the circuit is completed with the ground through his body. Current flows through his body resulting in a fatal shock.

 Question7. How can you charge a metal sphere negatively without touching it?

Solution. A metal sphere can be charged negatively without touching it by the process of induction.

 8. An insulating rod carries some net charge, and a copper sphere is neutral. The rod and the sphere not touch. Can there be a force of attraction/repulsion between the two?

Solution. When the charged rod is brought near the neutral sphere, the sphere gets oppositely charged by induction. Therefore, the sphere and the rod will attract each other. However, the force of repulsion between the two is not possible.

 9. Neutral metal objects, especially in industry, are often coated with electrically charged paint or powder particles. How do these particles stick to metal objects?

Solution. The electrically charged paint/powder particles charge the neutral metal surface oppositely by the process of polarization. The particles stick on the metal objects on account of the force of attraction between unlike charges.

 10. In figure shows two protons (symbol p) and one electron (symbol e) on a straight line AB. What is the direction of the net electrostatic force on the central proton?

Solution. The central proton is repelled by the other proton, along with BA; and it is attracted by electron again along with BA. Therefore, the net electrostatic force on the central proton is along with BA.