A solenoid has the following dimensions. inner diameter d = 4.22 cm length L= 42.7 cm When a current flows through the coil of the solenoid, the magnetic field inside the solenoid is 5.40 T. (a) Determine the magnetic energy density (in J/m³) in the field. UB= 1.16 X Apply the equation for the magnetic energy density and insert values. J/m³ (b) Determine the energy (in kJ) stored in the magnetic field within the solenoid. UB= kJ

1. A conducting loop of arca A and resistance R lics at right angles to a spatially uniform magnetic field. At time t = 0, the magnetic field and loop current are both zero. Subsequently, the current increases according to I (t) = bt², where b is a constant with units A/s?. Find an expression for the magnetic field strength as a function of time.

A stationary square coil of area 0.1 m2 is brought over time of 2 s into the magnetic field 8.9 T with its plane perpendicular to the magnetic field. The coil has 1030 turns. Calculate the magnetic flux linkage through the coil. Give your answer in SI units.

the loop is A ab The figure below shows a rectangular loop with a resistance of 6.7 2. The area of 0.0026 m². The magnetic field throughout the region is A = 48 T/s. How much current is induced in the loop, AB increasing at a rate of in units of milli-Amps (mA)? 24,96,91,88 X X Your Answer: Answer x X CO x X X * X X x X B

4. A square loop of wire of side 0.20 m has a total resistance of 0.60 2. The loop is positioned in a uniform magnetic field of 0.03 T directed into the page, as shown in the figure below. B (into page) X X X X X x X X X X X X X X X X -0.20 m- a Calculate the magnetic flux through the loop. The magnetic field strength now increases uniformly to 0.20 T in 0.50 s. b. Calculate the emf induced in the loop during this period. c. Calculate the current in the loop during this period. d. What is the direction of the current in the loop (clockwise or counterclockwise)? Justify your answer. 0.20 m

You have a solenoid with an initial current of 118 A and a turn density of 5365 What is the initial magnetic field through the solenoid? Binitial = T The current in the solenoid drops to 52 A over the course of 1.1 ms. What is the final magnetic field through the solenoid? Bfinal= T loops m Inside the solenoid is a coil with 74 loops and a radius of 7.9 cm. The coil is aligned so that the magnetic field from the solenoid passes through the coil perpendicular to the plane of the coil (directly down the center of the coil). What is the magnitude of the induced emf in the 74-turn coil at the center of the solenoid during this change in magnetic field? Enter you answer as a positive number. emf = The coil has a resistance of 20 2. What is the current through the coil? Icoil = A What is the power dissipated by the coil? Pcoil = W

A 38.5 mA current is carried by a uniformly wound air-core solenoid with 410 turns, a 19.5 mm diameter, and 13.0 cm length. (a) Compute the magnetic field inside the solenoid. μT (b) Compute the magnetic flux through each turn. T.m² (c) Compute the inductance of the solenoid. mH (d) Which of these quantities depends on the current? (Select all that apply.) magnetic field inside the solenoid magnetic flux through each turn inductance of the solenoid

A 41.0 mA current is carried by a uniformly wound air-core solenoid with 460 turns, a 16.5 mm diameter, and 12.5 cm length. (a) Compute the magnetic field inside the solenoid. HT (b) Compute the magnetic flux through each turn. T.m² (c) Compute the inductance of the solenoid. mH (d) Which of these quantities depends on the current? (Select all that apply.) O magnetic field inside the solenoid magnetic flux through each turn inductance of the solenoid

A planar coil of wire has a single turn. The normal to this coil is parallel to a uniform and constant (in time) magnetic field of 1.80 T. An emf that has a magnitude of 2.40 V is induced in this coil because the coil's area A is shrinking. What is the magnitude of AA/At, which is the rate (in m²/s) at which the area changes? Number i Units

A stationary square coil of area 0.1 m2 is brought over time of 2 s into the magnetic field 9.1 T with its plane perpendicular to the magnetic field. The coil has 2112 turns. Calculate the magnetic flux linkage through the coil. Give your answer in SI units.