A circular plane sheet of radius 10 cm is placed in a uniform electric field of \(5 \times 10^5\) N C\(^{-1}\), making an angle of 60° with the field. The electric flux through the sheet is:

• (A) \(1.36 \times 10^2\) N m²C\(^{-1}\)
• (B) \(1.36 \times 10^4\) N m²C\(^{-1}\)
• (C) \(0.515 \times 10^2\) N m²C\(^{-1}\)
• (D) \(0.515 \times 10^4\) N m²C\(^{-1}\)

Two parallel infinite line charges \(+\lambda\) and \(-\lambda\) are placed with a separation distance \(R\) in free space. The net electric field exactly mid-way between the two charges is:

• (A) zero
• (B) \(\frac{2\lambda}{\pi \varepsilon_0 R}\)
• (C) \(\frac{\lambda}{\pi \varepsilon_0 R}\)
• (D) \(\frac{\lambda}{2\pi \varepsilon_0 R}\)

An electric dipole of moment \(\vec{p}\) is placed in a uniform electric field \(\vec{E}\). Then

(i) the torque on the dipole is \(\vec{p} \times \vec{E}\).

(ii) the potential energy of the system is \(\vec{p} \cdot \vec{E}\).

(iii) the resultant force on the dipole is zero.

Choose the correct option.

• (A) (i), (ii) and (iii) are correct
• (B) (i) and (iii) are correct and (ii) is wrong
• (C) Only (i) is correct
• (D) (i) and (ii) are correct and (iii) is wrong

A parallel plate capacitor having area \(A\) and separated by distance \(d\) is filled by a copper plate of thickness \(b\). The new capacity is:

• (A) \(\frac{\varepsilon_0 A}{d + \frac{b}{2}}\)
• (B) \(\frac{\varepsilon_0 A}{2d}\)
• (C) \(\frac{\varepsilon_0 A}{d - b}\)
• (D) \(\frac{2\varepsilon_0 A}{d + \frac{b}{2}}\)

A parallel plate capacitor of capacitance 5 µF and plate separation 6 cm is connected to a 1 V battery and charged. A dielectric of dielectric constant 4 and thickness 4 cm is introduced between the plates of the capacitor. The additional charge that flows into the capacitor from the battery is:

• (A) 2 µC
• (B) 3 µC
• (C) 5 µC
• (D) 10 µC

A slab of material of dielectric constant \(K\) has the same area \(A\) as the plates of a parallel plate capacitor, and has thickness \(\frac{3}{4}d\), where \(d\) is the separation of the plates. The capacitance when the slab is inserted between the plates is:

• (A) \(\frac{\varepsilon_0 A}{d} \left( \frac{K + 3}{4K} \right)\)
• (B) \(\frac{\varepsilon_0 A}{d} \left( \frac{2K}{K + 3} \right)\)
• (C) \(\frac{\varepsilon_0 A}{d} \left( \frac{K}{K + 3} \right)\)
• (D) \(\frac{\varepsilon_0 A}{d} \left( \frac{4K}{K + 3} \right)\)

A wire has a resistance of 2.5 Ω at 28°C and a resistance of 2.9 Ω at 100°C. The temperature coefficient of resistivity of the material of the wire is:

• (A) \(1.06 \times 10^{-3}\) °C\(^{-1}\)
• (B) \(3.5 \times 10^{-2}\) °C\(^{-1}\)
• (C) \(2.22 \times 10^{-3}\) °C\(^{-1}\)
• (D) \(3.95 \times 10^{-2}\) °C\(^{-1}\)

Choose the correct combination of three resistances 1 Ω, 2 Ω and 3 Ω to get equivalent resistance \(\frac{11}{5}\) Ω.

• (A) All three are combined in parallel
• (B) All three are combined in series
• (C) 1 Ω and 2 Ω are in parallel and 3 Ω is in series with both
• (D) 2 Ω and 3 Ω are combined in parallel and 1 Ω is in series with both

A battery of emf 15 V and internal resistance of 4 Ω is connected to a resistor. If the current in the circuit is 2 A, the resistance of the resistor and terminal voltage of the battery will be:

• (A) 2.5 Ω, 6 V
• (B) 3.5 Ω, 6 V
• (C) 2.5 Ω, 7 V
• (D) 3.5 Ω, 7 V

Two cells \(\varepsilon_1\) and \(\varepsilon_2\) are connected in opposition to each other as shown in the figure. The cell \(\varepsilon_1\) is of emf 9 V and internal resistance 3 Ω. The cell \(\varepsilon_2\) is of emf 7 V and internal resistance 7 Ω. The potential difference between the points A and B is:

• (A) 8.4 V
• (B) 5.6 V
• (C) 7.8 V
• (D) 6.6 V