Uniform magnetic field B points out of the page, and lies within a circle of radius R = 4.18 m. An electron is placed at the top edge of the circle (at distance R above the center of the circle). If the magnitude of the dB magnetic field begins to decrease at a steady rate = -6.71 T/s, find the force felt by the electron, in N. dt The sign of the answer gives the direction of the force: positive to the right, negative to the left.
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- The magnetic field between the poles of a magnet has magnitude 0.510 T. A circular loop of wire with radius 1.30 cm is placed between the poles so the field makes an angle of 22.0° with the plane of the loop. What is the magnetic flux through the loop? Wb(a) A conducting loop in the shape of a square of edge length ℓ = 0.380 m carries a current I = 10.6 A as in the figure above. Calculate the magnitude and direction of the magnetic field at the center of the square.find magnitude ut and direction.b) If this conductor is reshaped to form a circular loop and carries the same current, what is the value of the magnetic field at the center? find magnitude and direction. magnitude µT directionThe magnetic field has been measured to be horizontal everywhere along a square path of sides a = 40 cm, as shown in figure. Along the bottom the average magnetic field is B₁ = 4.26x 10-5 T. Along the sides the average magnetic field is B₂ = 0.0741 T. The total current in the area that is surrounded by the square path is out of the page and of magnitude I = 9.63 A. B3 a) B3 = B₂ 11___ a B₁ What is the magnitude of the average magnetic field at the top? b) If the current was doubled and its direction was into the page, what would be the average magnetic field vector at the top? B3 k SI
- Problem 9: An oscillating vertically-oriented magnetic field is given by B(t) = Bosin(wt), with Bo = 0.69 T and w = 1.5 rad/s. Part (a) What is the magnetic flux, in webers, through a horizontal circle of radius 6 cm at t = 0? Numeric : A numeric value is expected and not an expression. Part (b) What is the time derivative of the magnetic flux, in webers per second, through this circle at t = 0? Numeric : A numeric value is expected and not an expression. do/dt = Part (c) What is the magnitude of the electric field, in newtons per coulomb, around the circumference of the circle at t = 0? Numeric : A numeric value is expected and not an expression. E =Figure (a) shows an element of length ds = 1.26 um in a very long straight wire carrying current. The current in that element sets up a differential magnetic field aB at points in the surrounding space. Figure (b) gives the magnitude dB of the field for points 3.6 cm from the element, as a function of angle between the wire and a straight line to the point. The vertical scale is set by dB = 60.0 pT. What is the magnitude of the magnetic field set up by the entire wire at perpendicular distance 3.6 cm from the wire? Number i Units dB (pT) dB₂ 0 μT (a) π/2 9 (rad) (b) Wire 2Nonuniform displacement-current density. The figure shows a circular region of radius R = 5.0 cm in which a displacement current is directed out of the page. The magnitude of the density of this displacement current is given by Jo (9 A/m2)(1-r/R), where r is the radial distance (r< R). What is the magnitude of the magnetic field due to the displacement current at (a) r = 2.5 cm and (b) r= 6.5 cm? R
- A circular region 4.00 m in radius is filled with an electric field perpendicular to the face of the circle. The magnitude of the field in the circle varies with radius and time as E(r, t) = Arcos (@t) where A = 1000. V/m² and w = 3.00 x 10⁹ s¨¹. What is the maximum value of the magnetic field at the edge of the region? i TA conducting cylinder has radius ?a and volume current density J1=κr in the direction of the axis of the cylinder where κ is known. It is coaxial with a conducting cylindrical shell which has inner radius b and outer radius c. Suppose we have already determined that the magnetic field outside both cylinders is zero. If the outer cylinder has a current density of J2=αr, find α. Find the magnetic field in each possible region B(r<a) = B(a<r<b) = B(b<r<c) =Q28.19 (a) How large a current would a very long, straight wire have to carry so that the magnetic field 2.00 cm from the wire is equal to 1.00 G (comparable to the earth’s northward-pointing magnetic field)? (b) If the wire is horizontal with the current running from east to west, at what locations would the magnetic field of the wire point in the same direction as the horizontal component of the earth’s magnetic field? (c) Repeat part (b) except the wire is vertical with the current going upward.
- A cube of edge length = 5.00 cm is positioned as shown in the figure below. A uniform magnetic field given by B = (4.9 î+ 4.0 ĵ + 3.0 k) T exists throughout the region. y l B (a) Calculate the magnetic flux through the shaded face. mWb (b) What is the total flux through the six faces? mWbA magnetic field of strength 0.25 T is directed perpendicular to a plane circular loop of wire of radius 23 cm. Find the magnetic flux through the area enclosed by this loop. T·m2In 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?