Please answer all parts SHOWING ALL STEPS CLEARLY EXPLAINING THE CONCEPTS AND STEPS TO SOLVE EACH QUESTION IN SIMPLE ENGLISH!! Also, please make sure all solutions are 100% correct. DO NOT USE CALCULUS CONCEPTS (Integration, Cross product, etc.) TO SOLVE ANY OF THESE QUESTIONS. Thank you very much!

#1: Explain in detail how to determine when to use the Pythagorean theorem to find Net magnetic field when solving a Net magnetic field problem versus just adding the magnitudes found using the equations for magnetic fields.

A capacitor with an initial potential difference of 50 V is discharged through a 106 resistor when a switch between them is closed at t=0. At t=2 s, the potential difference across the capacitor is 25 V. What is the capacitance of the capacitor? (1) 2.9x10-6F (2) 2.0x10-6F (3) 3.5x105F (4) 3.5x10-7F (5) 0.5F , A voltmeter has an internal resistance R = 1 M9 and is designed to measure difference of potentials up to 10 V. A student needs to measure a difference of potentials that can be as large as 50 V. The student vaguely recalls that this can be done by adding a resistor to the voltmeter and asks for your guidance: What should be the value of the additional resistor? Should it be connected in series with or parallel to the voltmeter? (1) 4.0 M52, series (2) 5.0 MB, series (3) 0.17 M9, parallel (4) 0.20 M9, parallel (5) Cannot be done (the max voltage rating of a voltmeter can only be decreased.) In the circuit shown in the figure, the capacitor has capacitance C = 15 /F and the resistor R = 120. The initial charge of the capacitor is go = 10 uC. The switch is closed at t = 0. At what time would the power dissipated by the +9o resistor be exactly one half of the initial power dissipated right after closing of R the switch? (1) 62 us (2) 180 us (3 125 AS (4) 260 us (5) 150 usTwo regions in space, Region 1 and Region 2, are separated by a gap of thickness - - - d d filled with a magnetic field of B pointing into the page, as shown in the figure. If d = 1 cm and B = 0.1 T, what is the minimum kinetic energy required for X XXX! an electron to penetrate from Region 1 into Region 2? Region 1 |x x x x Region 2 X X X X (1 1.4 x 10-14 J XXXX, (2) 2.8 x 10-14 J 1X X X Xi 2.1 x 10-14 J IX X X X 4) 3.5 x 10-14 J X X X X 5 4.2 x 10-14 J B