Problem 4: A conducting rod spans a gap of length L = 0.179 m and acts as the fourth side of a rectangular conducting loop, as shown in the figure. A constant magnetic field B = 0.45 T pointing into the paper is in the region. The rod is moving under an external force with an acceleration a = At2, where A = 6.5 m/s4. The resistance in the wire is R = 150 Q. X B R V Randomized Variables L = 0.179 m B = 0.45 T A = 6.5 m/s4 R = 150 Q Part (a) Express the magnitude of the magnetic flux going through the loop, , in terms of B, x and L. Expression : Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x Part (b) Express the speed of the rod, v, in terms of A and t. Assume v = 0 at t = 0. Expression : V = Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, A, B, d, g, h, i, j, L, m, P, t, x Part (c) Express the position of the rod, x, in terms of A and t. Assume x = 0 at t = 0. Expression : X = www

Problem 2 (Nodal Analysis): Find V. Express the result in polar form. j4 2 ll + V, 2/0° A (4 5Ω -j3 Q 3/45° A

A positive-oriented closed path yis formed by joining three straight lines. The first straight line is formed by the coordinates at = 0, y = 2 and 2 = 2, y = 2. The second straight line is formed by the coordinates a = 2, y = 2 and 2 = 2, y = 0. The third straight line is formed by the coordinates z = 2, y = 0 to z = 0, y = 2. Evaluate $(3y² + √(3y² + 2) dr + (3 (x + y)²) dy. Provide answer correctly rounded to 2 decimal places:

Problem 2: Using vectors, prove that the sum of the squares of the four sides of a paral- lelogram equals the sum of the squares of its two diagonals.