Type here to search Useful Constant Permittivity in vacuum: -8.854 x 10-12 C²/(N m²) Coulomb constant: ke-9 x 109 Nm²/C² Permeability of free space: o 4× 107 T-m/A Problem 1. (4 points) The general form of Ampère's law. An electric field is increasing with time as 40+30-1 (V/m) where t is time in second. The filed is confined to a square area with side d= 10 cm as shown in Fig. 1 and directed outward perpendicular to the plane of the figure. What is the magnitude of the magnetic field at the point P, r= 20 cm from the center of the square? (A) 0.5 27c2 (B) 1.5 2.7C2 (C) 2.0 2702 (D) 3.0 27c2 E P Figure 1. Time-dependent electric field in a square area. Problem 2. (4 points) The Ampère-Maxwell law. A 30-A current is charging a capacitor that has circular plates 5 mm in diameter. The plate separation is 4 mm. What is the magnetic field between the plates 1 mm from the center? (A) 1 mT (B) 2 mT (C) 3 mT (D) 6 mT F3 e & PrtScn Home End PgUp FG 57 FB F9 F10 F4

(c) An electric dipole consists of 0.003 kg spheres charged to ∓3e-09 C at the ends of a 0.16 m long non-conducting rod of mass 0.006 kg  The dipole rotates on a frictionless pivot at its center. The dipole is held perpendicular to a uniform electric field with a field strength 1000 V/m, then released. What is the dipole's angular velocity (in rad/s) at the instant it is aligned with the electric field? (HINT: Look up the moment of inertia of the rotating rod about its center and don't forget the rotational kinetic energy term (along with the other terms) when you set up your conservation of energy problem). a)0.0534 b)0.446 c)0.289 d)0.119 e)0.137 f)0.205 (d) Four 1.9e-08 C charges are held in location to form a perfect square with sides of length 0.1 m. Two of the charges from opposing corners are released simultaneously, the other two are held in place. The mass of each charge is 0.003 kg. How fast (in m/s) will the two released charges be moving when they are far, far away from…

In the figure below, the plane defined by y = x separates medium1 of permeability ur1 = 1 from medium2 of permeability ur2 = 4. If the magnetic field in medium1 is H1 = î 10 [A/m] and the surface current density is Js = & 4V2 + ŷ 4V2 [A/m] on the boundary; a) determine the surface normal îî2, y=x Medium1 b) find H2, Medium2 c) find B2. Solve the question by clearly writing all steps of mathematical operations with correct notation and specifying all formulas and units.

3. Thermal conductivity of a substance is measured as k = k, TIT, . Find an average value for thermal conductivity in the temperature range of T1 and T2. [Ans. = (k, /272 xT} 2 – T}/2) (T2 – T;) 1|