Concept explainers
The contribution to the circulation integral due to each segment of the loop, and the net current through the loop that must be present.
Answer to Problem 17PQ
The contribution of side 1 is
Explanation of Solution
Draw the figure for the system as shown below:
Refer to the above figure, consider a square loop
Write the general expression for Ampere’s Circuital Law for the given above figure as.
Here,
Substitute
Substitute
Substitute
Substitute
Conclusion:
Substitute
Further,simplify the above equation as.
Thus, contribution of side
Substitute
Further,simplify the above equation as.
Thus, contribution of side
Substitute
Further,simplify the above equation as.
Thus, the contribution of side
Substitute
Further,simplify the above equation as.
Thus, the contribution of side
Thus, the contribution of side 1 is
Want to see more full solutions like this?
Chapter 31 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- In Niels Bohr’s 1913 model of the hydrogen atom, the single electron is in a circular orbit of radius 5.29 × 10−11 m and its speed is 2.19 × 106 m/s. (a) What is the magnitude of the magnetic moment due to the electron’s motion? (b) If the electron moves in a horizontal circle, counterclockwise as seen from above, what is the direction of this magnetic moment vector?arrow_forwardA current loop with magnetic dipole moment is placed in a uniform magnetic field , with its moment making angle θ with the field. With the arbitrary choice of U = 0 for θ = 90°, prove that the potential energy of the dipole-field system is .arrow_forwardA particle moving downward at a speed of 6.0106 m/s enters a uniform magnetic field that is horizontal and directed from east to west. (a) If the particle is deflected initially to the north in a circular arc, is its charge positive or negative? (b) If B = 0.25 T and the charge-to-mass ratio (q/m) of the particle is 40107 C/kg. what is ±e radius at the path? (c) What is the speed of the particle after c has moved in the field for 1.0105s ? for 2.0s?arrow_forward
- Two long coaxial copper tubes, each of length L, are connected to a battery of voltage V. The inner tube has inner radius o and outer radius b, and the outer tube has inner radius c and outer radius d. The tubes are then disconnected from the battery and rotated in the same direction at angular speed of radians per second about their common axis. Find the magnetic field (a) at a point inside the space enclosed by the inner tube r d. (Hint: Hunk of copper tubes as a capacitor and find the charge density based on the voltage applied, Q=VC, C=20LIn(c/b) .)arrow_forwardA long, straight wire going through the origin is carrying a current of 2.90 A in the positive z-direction (see the figure attached). A current I flows in the +z-direction in a vertical rod that lies along the z-axis in an x y z coordinate space. A dashed-line circle of radius r is labeled vector B and lies in the x y plane. At a point a distance r = 1.10 m from the origin on the positive x-axis, find the magnitude and direction of the magnetic field. (a)magnitude of the magnetic field (in T) b) direction of the magnetic field +x-direction −x-direction +y-direction −y-direction +z-direction −z-direction At a point the same distance from the origin on the negative y-axis, find the magnitude and direction of the magnetic field. (c) magnitude of the magnetic field (in T) (d) direction of the magnetic field +x-direction −x-direction +y-direction −y-direction +z-direction −z-directionarrow_forwardThe Biot-Savart law gives the magnetic field due to a very short segment of current I: Ho I dsxî p2 dB = where ds is a vector that points in the direction of the current with magnitude equal to the length of the small segment and r is the vector from the small current segment to the point P where you want to find the -2.5 m j and ds = (-0.04 i – 0.03 j) m and I = 4A What is the magnetic field dB at point P due to just the small wire segment ? (The Biot-Savart law holds only if the segment ds is infinitetessimally small but should be a good approximation here since ds < r). ds I +y P +x +z (out)arrow_forward
- A physics lab instructor is working on a new demonstration. She attaches two identical conducting balls with mass m = 0.190 g to threads of length L as shown in the figure. There are two strings in the figure. The top of each string is connected to the ceiling, and both strings are connected at the same point. The bottom of each string is connected to a spherical mass labeled m. Both strings have length Land hang at an angle of θto the vertical, with the two strings on opposite sides of the vertical. Both balls have the same charge of 7.60 nC, and are in static equilibrium when θ = 4.55°. What is L (in m)? Assume the threads are massless. Draw a free-body diagram, apply Newton's second law for a particle in equilibrium to one of the balls. Find an equation for the distance between the two balls in terms of L and θ, and use this expression in your Coulomb force equation. m (b) What If? The charge on both balls is increased until each thread makes an angle of θ = 9.10° with the…arrow_forwardThe figure shows two very long, straight conductors with the indicated electrical currents. Conductor 1 coincides with the "x" axis and conductor 2 is parallel to the "z" axis and passes through point A (0, 3, 0) cm. Determine the magnetic field vector at the point P (2, 3, 0) cm.arrow_forwardThe magnetic force acting on a straight wire carrying current I of length L in a uniform magnetic field B is given by F = IL x B, where L has length L and is pointing in the direction of the current. Consider the loop centered at the origin shown in the figure below. y= 4-x* for -24x42 -2 2 (b) The torque with respect to a pivot point is defined by the cross product of the separation vector i which is oriented from the pivot point to the point where the force acts and the force, チ=チxF. Find the torque acting on this loop with respect to the origin as the pivot point.arrow_forward
- In this problem we will use a 3-dimensional Cartesian coordinate system with coordinates x, y and z. In the cylindrical region defined by the inequality x2 + y2 < R2 the magnetic field is zero, while outside the cylindrical region the magnetic field points in the +z direction and has constant magnitude B. From the origin of our coordinate system an electron starts with velocity v0= eBR/m in the positive x direction (here e is the elementary charge and m is the mass of the electron). Sketch the trajectory of the electronand find the period of its motion.arrow_forwardA wire with total resistance R is formed into a circle. This circle is placed horizontally (in the x-y plane) within the constant magnetic field in the +Zdirection. The change of the radius of the circle with respect to time is expressed by r= ra(1+3t). The circle begins to expand at the moment t = 0. (Assume that the resistance R does not change in this process). For t=1s, find the magnitude and direction of the current formed in the circle. (R= 5 Ohm, 3 = 3TR, n =1cm )arrow_forwardA circular loop of wire (radius a) carrying a steady current I is centered at the origin in the x − z plane. The loop is then bent 90◦ along the x-axis, so that the lower half now lies in the x − y plane. Find the magnetic field at a point on the z-axis for the bent loop. assuming z >> a.arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning