Q.1 Charges𝐐, 𝟐𝐐 and −𝐐 are given to three concentric conducting spherical shell𝐀, 𝐁 and 𝐂 respectively as shown in figure. The ratio of charges on the inner and outer surfaces of shell 𝐂 will be (A)+ Q.2 3 4 −4Q 3 (D)− (C) 4 2 3 2 13 −8Q (B) −5Q (C) 11 −3Q (D) 3 7 Two concentric thin conducting spherical shells having radius 𝐑 and 𝟐𝐑 are shown in figure. A charge +𝐐 is given to shell 𝐀 and −𝟒𝐐 is given to shell𝐁. Now shell 𝐀 and 𝐁 are connected by a thin conducting wire, then the final charge on the sphere 𝐁 will be: −3Q (A) Q.4 3 Figure shows a system of three concentric metal shells𝐀, 𝐁 and 𝐂 with radii𝐚, 𝟐𝐚 and 𝟑𝐚 respectively. Shell 𝐁 is earthed and shell 𝐂 is given a charge𝐐. Now, if shell 𝐂 is connected to shell𝐀, then the final charge on the shell 𝐁 is equal to (A) Q.3 (B)− 2 (B)−4Q (C)−3Q (D)2Q Two large conducting sheets are kept parallel to each other as shown in the figure. In equilibrium, the charge density on facing surfaces is 𝛔𝟏 and𝛔𝟐 . What is the net value of electric field at𝐀 ? σ1 (A) ϵ0 i (B)− σ2 ϵ0 σ 1 +σ 2 i (C) 1 2ϵ0 i σ 1 −σ 2 (D) 2ϵ0 i Q.5 An uncharged conducting large plate is placed as shown in the figure below. Now a uniform electric field 𝐄 towards right is applied. Find the induced charge density on the right surface of the plate. (A)−ε0 E Q.6 (B)ε0 E (D)2ε0 E A large charged conducting sheet is placed in a uniform electric field, perpendicularly to the electric field lines. After placing the sheet into the field, the electric field on the left side of the sheet is 𝐄𝟏 = 𝟓 × 𝟏𝟎𝟓 𝐕/𝐦 and on the right it is 3.6𝜋 × 10−2 𝑚2 𝐄𝟐 = 𝟑 × 𝟏𝟎𝟓 𝐕/𝐦. The sheet experiences a net electric force of𝟎. 𝟎𝟖 𝐍. Find the area of one face of the sheet. (Assume the external field to remain constant after introducing the large sheet) 𝐤= 𝟏 𝟒𝛑𝛆𝟎 = 𝟗 × 𝟏𝟎𝟗 𝐍𝐦𝟐 𝐂−𝟐 𝐯 (A)3.6π × 10−2 m2 Q.7 (C)−2ε0 E (B)0.9π × 10−2 m2 (C)1.8π × 10−2 m2 (D)None Three identical large plates are placed parallel to each other at a very small separation as shown in the figure. The central plate is given a charge𝐐. What amount of charge will flow to earth when the key is closed. (The other two plates are initially neutral) (A)– Q (B)+2Q (C)+Q (D)−2Q 2 Q.8 Two conducting plates 𝐀 and 𝐁 are placed parallel to each other. 𝐀 And 𝐁 are given charges 𝟏𝟎 𝐧𝐂 and 𝟏𝟐 𝐧𝐂 respectively. Find the distribution of charge on the inner surface of plate𝐀. (A)−1nC (B)−2nC (C)−2nC (D)−3Nc Q.9 Determine the current flowing (in 𝐀) through an element at time 𝐭 = 𝟐 𝐬𝐞𝐜⁡ , if the charge flow is 𝟐 given by 𝐪 = (𝟐𝐭 + 𝟑) C. (A)1 (B)2 (C)4 (D)8 Q.10 The current through a wire depends on time as𝐈 = (𝟐 + 𝟑𝐭) 𝐀. Calculate the charge crossed through a cross-section of the wire in 𝟏𝟎 𝐬. (A)170 C (B)70 C (C)150 C (D)20 C Q.11 A conducting sphere 𝐀 of radius 𝐚, with charge𝐐, is placed concentrically inside a conducting shell 𝐁 of radius𝐛. 𝐁 is earthed and 𝐂 is the common center of 𝐀 and 𝐁. Study the following statements. 𝐼. The potential at a distance 𝐫 from𝐂, where 𝐚 ≤ 𝐫 ≤ 𝐛, is 𝟏 𝐐 𝟒𝛑𝛜𝟎 𝐫 𝐼𝐼. The potential difference between 𝐀 and 𝐁 is 𝐐 𝟏 𝟏 − 𝟒𝛑𝛜𝟎 𝐚 𝐛 𝐼𝐼𝐼.The potential at a distance 𝐫 from𝐂, where 𝐚 ≤ 𝐫 ≤ 𝐛, is 𝐐 𝟏 𝟒𝛑𝛜𝟎 𝐫 (A)Only I and II − 𝟏 𝐛 (B)Only II and III (C)Only I and III 3 (D)All Q.12 Three large identical conducting parallel plates carrying charge+𝐐,−𝐐 and +𝟐𝐐 respectively, are placed as shown in the figure. If 𝐄𝐀 , 𝐄𝐁 and 𝐄𝐂 refer to the magnitudes of the electric fields at points 𝐀, 𝐁 and 𝐂 respectively, then (A)EA > EB > EC (B)EA = 0 and Ec > EB (C)EA = 0 and EB > EC (D)EA = 0 and EB = EC 4