Question

11. (a) Consider two metal plates with equal but opposite charges +Qand - as in Fig. 11(a), separated by a distance d. Sketch the charge distribution within the positively-charged plate. Note that the plate should have finite thickness in your diagram. (2 marks) ii. What is the magnitude of the electric field inside a conductor? Explain briefly your answer. (2 marks) iii. By constructing a suitable Gaussian surface, and use the answers in (i) and (ii), show that the potential difference in the space between the metal plates is given by AV = "", where a is the surface charge density. (3 marks) (b) The setup in Fig. 11(a) is placed in a uniform magnetic field B (Fig. 11(b), shaded region) that runs perpendicular to the plane of the paper. A proton beam enters the space between the plates with an initial velocity v parallel to the metal plates and in the plane of the paper. Charges on the plates remain unchanged. Show that the condition for undeflected motion of the protons is v; = For the undeflection motion, decide whether the magnetic field runs out of the paper or into the paper, and briefly explain your answer. (4 marks) The beam is introduced in the middle of the two plates and d=5 mm, L= 10 cm. Assume the magnetic force is directed opposite to the electric forcethroughout its journey in the shaded region. If V - 50 V, B = 0.3 T, what is the minimum proton beam velocity such that they can avoid hitting on the plates? (4 marks) L Fig. 11(a) +Q -Q +Q 1 -Q Fig. 116)

Answer 1

ਉਚਾਚੇ ਨੇ । gooo0000000000000 line magnitude of electric feild Insicle a Conducts is zero, because of the uniform distoolhon of chiage on the Surfure of metallu) net clectic fould Cets Cancelled Out - And here is no presenie Inosile a Conduchs. CPlates ?

Worte the expression to the Good law is the two choosed plutes, De Gauron sto face & Consoclencel to be Rechunjoles to each plate. yyyy - 4. on sa - EA E s. Cos 0 = 1.7 - & A-GA (0-6A] > EE -0 The Potended defferne byw the plates is (2_) AV - - Pe. as -Ed 6 Foom ee- Pave

v Understand thart for of stand that for the unceflee lead Mohon of the Proton bw the chorged Plutes. Uncles de feid is poomble, if the frore applied by electre feild and magnehe teinud cre equal. APAAAAA O É - Ovi B Sino E = Q vil CO- Goo] WE - AND Like daer hon of Magne he feild is into the Paper, Uong the Right hand Rule, Disechon of Magrane fosse is opponte to eleitor Dhecht frore.

ا ت ) Ao cloned in revious post 110; bus. woon here, vi i see minimun Boden beam relocity r = sor (032) Spe)ko m ex5x109 Vi= 0.333._ x 103 m2,