If the magnetic field steadily decreases from B to zero during a time interval t, what is the magnitude I of the induced current? Express your answer in terms of x, y, B, t, and the resistance R of the wire

A straight conductor of length L moves with an acceleration A =0.1 ms-2 at right angles to a magnetic field of uniform strength B=10.2 T. Calculate L, considering that the e.m.f., ? = BLv, between the ends of the conductor increased from 0 to 5 V during the first 20 s after the beginning of motion.

A uniform externally applied magnetic field is in the +z direction (B = Bk, with B positive) and B is increasing with time. A loop of wire in the x-y plane is in this field (the magnetic field is perpendicular to this loop); it has a total resistance R independent of the radius r of the loop. Which of the following statements is true? The magnitude of the current is proportional to the radius of the loop: I=αr, α a constant.  The current at any time is proportional to the magnitude of the magnetic field at that time.  The current induced in the wire will produce a magnetic field in the –z direction. None of a-c More than one of a-c

For a physics lab assignment, a student needs to create a solenoid using copper wire with diameter d = 0.500 mm. The resistance of the solenoid needs to be 3.50 and the magnetic field of the solenoid with a current of 2.90 A should be 5.90 × 10-² T. Assume the resistance does not change significantly with temperature, and the radius of the solenoid is 1.00 cm. (Use p 1.70 x 10-8.m for the resistivity of copper.) (a) How many turns of wire does the student need? turns (b) Determine the required length (in cm) of the solenoid. cm

Three long parallel wires, lie perpendicular to this page, as shown in the figure, and carry the same current intensity I = 2 A. The current along the wire A is going into the page. The current along the wire B is also going into the page. The current along the wire C is coming out of the page. Knowing that d = 1 cm, find the direction and magnitude of the net force per unit length acting on the wire B. (Force per unit length just means divide the force by the length.) 2d d A В

Given: B = 5 * 10-5 T ẑ; σ = 4 (Ohm-meters)-1 (conductivity) a) Assume that seawater is moving at a constant velocity v = v0 ŷ and that the Earth’s magnetic field is along the ẑ-direction. Calculate the electric current density J produced by the magnetic force. Hint: first compute the force per unit charge, F/q, and then use the relationship J = σ(F/q).  b) Derive the equation of motion of a cylindrical differential volume element of base area δA and height δh parallelto the direction of J. Assume that seawater has a known volumetric mass density ρ. Show that this equation implies that the velocity satisfies the following differential equation:dvy/dt = vy/τwhere τ is a constant that you should write in terms of B, σ, and ρ.

Consider the RL direct current circuit shown. The circuit contains R = 4.0 Ω,  L = 10 mH, &  ε = 12 V. The circuit is charging. (a) Determine the time constant for the circuit? (b) What is the maximum current in the circuit? (c) What is the current one time constant (t = τ )? (d) When the current is 0.5 A, what is the strength of the magnetic field in the solenoid, with n = N/ℓ = 319x103 turns/m.  (    T×m/A)

Find the flux of the Earth's magnetic field of magnitude 5.00 ✕ 10-5 T, through a square loop of area 30.0 cm2 for the following. (a) when the field is perpendicular to the plane of the loop T·m2(b) when the field makes a 30.0° angle with the normal to the plane of the loop T·m2(c) when the field makes a 90.0° angle with the normal to the plane T·m2