Figure (a) shows an element of length d, = 1.00 µm in a very long straight wire carrying current. The current in that element sets up a differential magnetic field dB at points in the surrounding space. Figure (b) gives the magnitude dB of the field for points 2.7 cm from the element, as a function of angle e between the wire and a straight line to the point. The vertical scale is set by dB; = 61.1 pT. What is the magnitude of the magnetic field set up by the entire wire at perpendicular distance 2.7 cm from the wire?

. A solenoid has radius 5.80 mm, length 11.0 cm, 5000 turns, and is placed with its axis of symmetry along the x-axis, through the origin. A vector normal to the opening of the solenoid points to the right. We measure the resistance of the solenoid to be 14.0 Ω. The solenoid is in a region where the temperature is 49.0°C and initially, there is an external magnetic field of 0.30 T in the +x direction. Then the magnetic field is turned off and drops to 0 T over 50.0 milliseconds a. What is the magnitude of the average induced emf during the 50.0 milliseconds while the magnetic field magnitude decreases to 0?  b. What is the direction of the induced current, as viewed from the right? Answer clockwise, counterclockwise, or zero and show work or explain in words.  c. What is the magnitude of the induced current?  d. What is the magnitude and direction of the induced magnetic field?

The diagram below is of a triangular prism that has three rectangular sides and two triangular sides. This prism is placed in a region of uniform magnetic field of magnitude 0.120 T directed in the positive x direction. Here ab = 30.0 cm, ac = 40.0 cm, bc 50.0 cm, and ad 66.0 cm. = = = = Determine the magnetic flux, including the sign, through each of the five faces of the box. abc cbef Pabed Pacfd def = Additional Materials = Reading B a Wb Wb Wb Wb Wb y

In a given region of space, the vector magnetic potential is given by A = x5 coszy + z(0.2+ sin zx) mWb/m. The magnetic flux passing through a square loop with 0.25 cm long edges if the loop is in the x-y plane, its center is at the origin, and its edges are parallel to the x- and y- axis?

An infinite length line carries current I in the +az direction on the z-axis, and this is surrounded by an infinite length cylindrical shell (centered about the z-axis) of radius a carrying the return current I in the -az direction as a surface current. Find expressions for the magnetic field intensity everywhere. If the current is 1.0 A and the radius a is 2.0 cm, plot the magnitude of H versus radial distance from the z-axis from 0.1 cm to 4 cm.

A square wire with side a = 0.085 m is in a time-varying magnetic field with magnitude B(t) = At, where A = 0.15 T/s. The plane in which the square is located has an angle θ with the direction of B. Express the magnitude of the magnetic flux going through the loop, Φ, in terms of A, t, a and θ.  a. Express the derivative of the flux with respect of time, dΦ/dt.  b. Express the magnitude of the emf induced in the loop, ε, in terms of A, a, and θ.  c. Calculate the numerical value of ε when θ = 0, in volts.  d. Calculate the numerical value of ε when θ = 90°, in volts.

The magnetic field in a region of space is given by B-8 +8. A coil of N turns is oriented so that its cross-sectional area is in the x direction: A-A1. A small bulb is connected across the ends of the coil. The total resistance of the coil and the bulb is R. Find an expression for the current through the bulb if By(t) = Bo(t/to) and By-Bo where Bo and to are constants. (Use the following as necessary: A, B, N, R, to, and t. Enter the magnitude.)