Chapter 29: Problem 9
When you plug a refrigerator into a wall socket, on occasion, a spark appears between the prongs. What causes this?
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Chapter 29: Problem 9
When you plug a refrigerator into a wall socket, on occasion, a spark appears between the prongs. What causes this?
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Two parallel conducting rails with negligible resistance are connected at one end by a resistor of resistance \(R\), as shown in the figure. The rails are placed in a magnetic field \(\vec{B}_{\text {ext }},\) which is perpendicular to the plane of the rails. This magnetic field is uniform and time independent. The distance between the rails is \(\ell\). A conducting rod slides without friction on top of the two rails at constant velocity \(\vec{v}\). a) Using Faraday's Law of Induction, calculate the magnitude of the potential difference induced in the moving rod. b) Calculate the magnitude of the induced current in the \(\operatorname{rod}, i_{\text {ind }}\). c) Show that for the rod to move at a constant velocity as shown, it must be pulled with an external force, \(\vec{F}_{\mathrm{ext}},\) and calculate the magnitude of this force. d) Calculate the work done, \(W_{\text {ext }},\) and the power generated, \(P_{\text {ext }}\), by the external force in moving the rod. e) Calculate the power used (dissipated) by the resistor, \(P_{\mathrm{R}}\). Explain the correlation between this result and those of part (d).
A solenoid with 200 turns and a cross-sectional area of \(60 \mathrm{~cm}^{2}\) has a magnetic field of \(0.60 \mathrm{~T}\) along its axis. If the field is confined within the solenoid and changes at a rate of \(0.20 \mathrm{~T} / \mathrm{s}\), the magnitude of the induced potential difference in the solenoid will be a) \(0.0020 \mathrm{~V}\). b) \(0.02 \mathrm{~V}\). c) \(0.001 \mathrm{~V}\). d) \(0.24 \mathrm{~V}\).
Large electric fields are certainly a hazard to the human body, as they can produce dangerous currents, but what about large magnetic fields? A man \(1.80 \mathrm{~m}\) tall walks at \(2.00 \mathrm{~m} / \mathrm{s}\) perpendicular to a horizontal magnetic field of \(5.0 \mathrm{~T} ;\) that is, he walks between the pole faces of a very big magnet. (Such a magnet can, for example, be found in the National Superconducting Cyclotron Laboratory at Michigan State University.) Given that his body is full of conducting fluids, estimate the potential difference induced between his head and feet.
A solid metal disk of radius \(R\) is rotating around its center axis at a constant angular speed of \(\omega .\) The disk is in a uniform magnetic field of magnitude \(B\) that is oriented normal to the surface of the disk. Calculate the magnitude of the potential difference between the center of the disk and the outside edge.
A circular conducting loop with radius \(a\) and resistance \(R_{2}\) is concentric with a circular conducting loop with radius \(b \gg a(b\) much greater than \(a\) ) and resistance \(R_{1}\). A time-dependent voltage is applied to the larger loop, having a slow sinusoidal variation in time given by \(V(t)=V_{0} \sin \omega t\) where \(V_{0}\) and \(\omega\) are constants with dimensions of voltage and inverse time, respectively. Assuming that the magnetic field throughout the inner loop is uniform (constant in space) and equal to the field at the center of the loop, derive expressions for the potential difference induced in the inner loop and the current \(i\) through that loop.
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