A rod with resistance R lies across frictionless conducting rails in a constant uniform magnetic field B, pointing into the paper as shown below. Assume the rails have negligible resistance. The magnitude of the force that must be applied by a person to pull the rod to the right at constant speed vis:
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- Suppose that there is a magnetic field B Cartesian coordinate system with ê x ŷ = î. For all the discussions below, ignore the units. = 3xî filling a 3D space. The coordinates are set up as a a) Find the expression for the magnetic force on a positive charge +Q that is located at 7 = (2,1, –1) and moving at velocity i = (2,3,1) b) In this magnetic field, is it possible for any particle to move along a circular path? If so, indicate the conditions for the position and the velocity of the particle; If not, briefly explain your reasons.Determine the magnitude of the magnetic fieldmidway between two long straight wires separatedby a distance d if one carries current I- when theother carries I2. Assume It> 12 Assume these currents are in the same direction.Express your answer in terms of the variables d, I1, I2, and appropriate constants.An observation point, PP, is located a perpendicular distance, RR, from one endpoint of a segment of wire that carries a current, II. The wire is very long compared to the distance RR, so it may be treated as if it is infinitely long. (You may assume that this segment is part of a larger circuit that may be ignored for the purposes of this exercise.) You will calculate the magnetic field at the point PP by evaluating a Biot-Savart integral of the form A) Enter an expression for the current element B) With the origin of your coordinate system placed at the point P, enter an expression for the unit vector r hat, . C) With the origin of your coordinate system placed at the point P, enter an expression for r. D) With the origin of your coordinate system at the observation point P, which integral provides a correct expression of the magnetic field, B(vector), evaluated at P? (Make no simplifications at this step.) E) Evaluate the integral and enter a simplified expression for the…
- Calculate the magnetic field at point O for the current-carrying wire segment shown. The wire consists of two straight portions and a circular arc of radius a, which subtends an angle θ.Derive the magnetic field of an infinitely long straight coaxial cable that carries the same current in opposite directions in its conductors. Introduce generic radii of the conductors as needed. Make a sketch.Write down an expression for the net force along the (tangentially to) arc of motion on a simple pendulum made of a metal rod of the length l and the mass m carrying the current I . The rod is suspended by the middle on a weightless wire of the length L in the magnetic field B and the gravitational field g perpendicular to the rod (see picture below).
- A conducting rod is free to move along 2 parallel conducting rails. On one end a resistor, R, connects the two rails which forms a circuit. The rails are oriented along the y axis of a coordinate system. There is a constant magnetic B aligned with the z axis making it perpendicular to the plane of the rails and rod. If the rod is given an initial velocity of vo, and hence a kinetic energy of m*vo2 /2, mathematically demonstrate that as the rod rounds to a stop in an infinite time the power lost in the resistor as heat is equal to the initial kinetic energy.A single circular loop of radius 0.23 m carries a current of 2.6 A in a magnetic field of 0.95 T. Find the angle the plane of the loop must make with the field if the torque is to be half its maximum value. Express your answer using two significant figures.A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in the figure below. (a) Determine the magnetic flux through the loop due to the current I. (Use any variable stated above along with the following as necessary: Ho:) (b) Suppose the current is changing with time according to I = a + bt, where a and b are constants. Determine the magnitude of the emf (in V) that is induced in the loop if b = 16.0 A/s, h = 1.00 cm, w = 20.0 cm, and L = 1.35 m. v (c) What is the direction of the induced current in the rectangle? clockwise counterclockwise The magnitude is zero. What If? Suppose a constant current of I = 6.00 A flows in the straight wire and the loop moves from an initial position ho = 1.00 cm toward the bottom of the figure at a constant speed of v = 18.0 cm/s. (d) What is the magnitude of the induced emf (in V) in the loop 1.00 s after it begins to move? (e) What is the direction of the induced…
- A 6A current flows in a wire as shown. The radius of the arc is 0.5m, and the length of each of the straight wires is 1.37m. If the arc subtends an angle of 125 degrees, determine the magnitude of the magnetic field at its center. [give your answer in units of microTeslas with 2 decimal places of precision]If two magnetic field vectors H, and H2 are moving along the same axis in free space, write all the possible base vectors.A coaxial cable consists of two very long cylindrical tubes, separated by linear insulating material of mag- netic susceptibility Xm, A current I flows down the inner conductor and returns along the outer one. The current is uniformly distributed in each case. Find the magnetic field in the region between the tubes.