Answer:
Certainly, let's break down the solutions to each question:
35) The units of the electric field are measured in Newton per Coulomb per meter (N/C or J/C·m). Electric field represents the force experienced by a unit positive charge placed in the field. The correct answer is (d) J/m.
36) The electric field (\(E\)) between two point charges is given by the formula \(E = k \cdot \frac{{q_1 - q_2}}{{r^2}}\), where \(k\) is the electrostatic constant (9 × 10^9 N·m^2/C^2), \(q_1\) and \(q_2\) are the charges, and \(r\) is the distance between them. Midway between them, the charges add up, so \(E = 9 × 10^9\) N/C. The correct answer is (b) \(9 \times 10^{9}\).
37) The volume charge density (\(\rho\)) is defined as the charge per unit volume (\(\rho = \frac{Q}{V}\)). In this case, the total charge (\(Q\)) is given, and the volume (\(V\)) of the sphere is \(\frac{4}{3} \pi r^3\), where \(r\) is the radius. Substituting the values, we get \(\rho = 3.7 \times 10^{-7}\) C/m³. The correct answer is (a) \(3.7 \times 10^{-7}\) C/m³.
38) The electric flux (\(\Phi\)) through a closed surface is given by \(\Phi = \frac{Q}{\varepsilon_0}\), where \(Q\) is the total charge enclosed by the surface, and \(\varepsilon_0\) is the permittivity of free space (8.85 × 10^-12 C²/N·m²). In this case, \(Q\) is given as 5.0 μC (5.0 × 10^-6 C). Substituting the values, we get \(\Phi = 9.4 \times 10^4\) N·m²/C. The correct answer is (c) \(9.4 \times 10^4\) N·m²/C.
39) The electric field (\(E\)) at a point inside a uniformly charged sphere is given by \(E = k \cdot \frac{Q}{r^2}\), where \(k\) is the electrostatic constant, \(Q\) is the total charge of the sphere, and \(r\) is the distance from the center. In this case, \(r = \frac{R}{2}\). Substituting the values, we get \(E = \frac{Q}{4 \pi \varepsilon_0 R^2}\). The correct answer is (a) \(\frac{Q}{4 \pi \varepsilon_0 R^2}\).
40) The acceleration (\(a\)) of a charged particle in an electric field is given by \(a = \frac{F}{m}\), where \(F\) is the force experienced by the particle, and \(m\) is the mass of the particle. The force (\(F\)) is given by \(F = qE\), where \(q\) is the charge of the electron and \(E\) is the electric field. Substituting the values, we get \(a \approx 5.3 \times 10^{10}\) m/s². The correct answer is (a) \(5.3 \times 10^{10}\) m/s².