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<h2 class="hd hd-2 unit-title">Question 10.1</h2>
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<h2>question 10.1</h2>
<p>An inductive recording head can be modeled as a permalloy core with a gap in it, threaded by copper coils. </p>
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<b> Part A </b>
<p>From the geometry sketched below, derive the field at the gap, \(H_{gap}\), as a function of coil current \(i\). (Permalloy has a low hysteresis. Assume a linear \(B-H\) relation until it saturates.)<br/><br/> Please remember that you need to express multiplication explicitly by typing '*'; therefore, if your answer were \(84i\), you would need to type '84*i' into the box below.<br/><br/></p>
<p>\(H_{gap}\) in (\(A/m\)):</p>
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<b>Part B</b>
<p>If the saturation induction (\(B_{sat}\)) of permalloy is \(1 T\), what is the maximum field \(H_{gap}\) which can be achieved?</p>
<p>\(H_{gap}\) (in \(A/m)\)):</p>
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<p>What coil current is needed to achieve this field?</p>
<p>\(i\) (in \(mA\)):</p>
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<p>It is possible to use this head for reading the disk as well as for writing. If the disk is spinning at \(10,000\) rpm, its radius is \(5 cm\), the bit length is \(0.2 \mu m\), and the maximum field emanating from the bit is \(1000 A/m\), estimate the readback voltage which the head produces. The cross-sectional area of the gap in the head is \(2 \times 10^{-12} m^2\).</p>
<p>\(V\) (in \(\mu V\)):</p>
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<h3 class="hd hd-3 problem-header" id="7b966362175f4e719aaf1a040615804d-problem-title" aria-describedby="block-v1:MITx+3.15.3x+2T2017+type@problem+block@7b966362175f4e719aaf1a040615804d-problem-progress" tabindex="-1">
Question 10.2
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<p>We discussed heat assisted magnetic recording (HAMR) and bit-patterned media (BPM) as two options for extending hard drive densities. Indicate which factors are significant in limiting the ultimate density that can be achieved with HAMR, and which are significant in limiting the density that can be achieved with BPM. Consider the media itself as well as the read-write head.</p>
<p>HAMR Limits:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_7b966362175f4e719aaf1a040615804d_2_1">
<fieldset aria-describedby="status_7b966362175f4e719aaf1a040615804d_2_1">
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<input type="checkbox" name="input_7b966362175f4e719aaf1a040615804d_2_1[]" id="input_7b966362175f4e719aaf1a040615804d_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="7b966362175f4e719aaf1a040615804d_2_1-choice_0-label" for="input_7b966362175f4e719aaf1a040615804d_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_7b966362175f4e719aaf1a040615804d_2_1"> Head stability during laser operation
</label>
</div>
<div class="field">
<input type="checkbox" name="input_7b966362175f4e719aaf1a040615804d_2_1[]" id="input_7b966362175f4e719aaf1a040615804d_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="7b966362175f4e719aaf1a040615804d_2_1-choice_1-label" for="input_7b966362175f4e719aaf1a040615804d_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_7b966362175f4e719aaf1a040615804d_2_1"> Laser switching time
</label>
</div>
<div class="field">
<input type="checkbox" name="input_7b966362175f4e719aaf1a040615804d_2_1[]" id="input_7b966362175f4e719aaf1a040615804d_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="7b966362175f4e719aaf1a040615804d_2_1-choice_2-label" for="input_7b966362175f4e719aaf1a040615804d_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_7b966362175f4e719aaf1a040615804d_2_1"> Lithography resolution
</label>
</div>
<div class="field">
<input type="checkbox" name="input_7b966362175f4e719aaf1a040615804d_2_1[]" id="input_7b966362175f4e719aaf1a040615804d_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="7b966362175f4e719aaf1a040615804d_2_1-choice_3-label" for="input_7b966362175f4e719aaf1a040615804d_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_7b966362175f4e719aaf1a040615804d_2_1"> Curie temperature compared with the temperature distribution on the disk
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</div>
<div class="field">
<input type="checkbox" name="input_7b966362175f4e719aaf1a040615804d_2_1[]" id="input_7b966362175f4e719aaf1a040615804d_2_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="7b966362175f4e719aaf1a040615804d_2_1-choice_4-label" for="input_7b966362175f4e719aaf1a040615804d_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_7b966362175f4e719aaf1a040615804d_2_1"> Ability to track bits
</label>
</div>
<div class="field">
<input type="checkbox" name="input_7b966362175f4e719aaf1a040615804d_2_1[]" id="input_7b966362175f4e719aaf1a040615804d_2_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="7b966362175f4e719aaf1a040615804d_2_1-choice_5-label" for="input_7b966362175f4e719aaf1a040615804d_2_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_7b966362175f4e719aaf1a040615804d_2_1"> Ability to synchronize the write field with the location of bits
</label>
</div>
<span id="answer_7b966362175f4e719aaf1a040615804d_2_1"/>
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<p>Bit-Patterned Media Limits:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_7b966362175f4e719aaf1a040615804d_3_1">
<fieldset aria-describedby="status_7b966362175f4e719aaf1a040615804d_3_1">
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<input type="checkbox" name="input_7b966362175f4e719aaf1a040615804d_3_1[]" id="input_7b966362175f4e719aaf1a040615804d_3_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="7b966362175f4e719aaf1a040615804d_3_1-choice_0-label" for="input_7b966362175f4e719aaf1a040615804d_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_7b966362175f4e719aaf1a040615804d_3_1"> Head stability during laser operation
</label>
</div>
<div class="field">
<input type="checkbox" name="input_7b966362175f4e719aaf1a040615804d_3_1[]" id="input_7b966362175f4e719aaf1a040615804d_3_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="7b966362175f4e719aaf1a040615804d_3_1-choice_1-label" for="input_7b966362175f4e719aaf1a040615804d_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_7b966362175f4e719aaf1a040615804d_3_1"> Laser switching time
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<div class="field">
<input type="checkbox" name="input_7b966362175f4e719aaf1a040615804d_3_1[]" id="input_7b966362175f4e719aaf1a040615804d_3_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="7b966362175f4e719aaf1a040615804d_3_1-choice_2-label" for="input_7b966362175f4e719aaf1a040615804d_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_7b966362175f4e719aaf1a040615804d_3_1"> Lithography resolution
</label>
</div>
<div class="field">
<input type="checkbox" name="input_7b966362175f4e719aaf1a040615804d_3_1[]" id="input_7b966362175f4e719aaf1a040615804d_3_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="7b966362175f4e719aaf1a040615804d_3_1-choice_3-label" for="input_7b966362175f4e719aaf1a040615804d_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_7b966362175f4e719aaf1a040615804d_3_1"> Curie temperature compared with the temperature distribution on the disk
</label>
</div>
<div class="field">
<input type="checkbox" name="input_7b966362175f4e719aaf1a040615804d_3_1[]" id="input_7b966362175f4e719aaf1a040615804d_3_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="7b966362175f4e719aaf1a040615804d_3_1-choice_4-label" for="input_7b966362175f4e719aaf1a040615804d_3_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_7b966362175f4e719aaf1a040615804d_3_1"> Ability to track bits
</label>
</div>
<div class="field">
<input type="checkbox" name="input_7b966362175f4e719aaf1a040615804d_3_1[]" id="input_7b966362175f4e719aaf1a040615804d_3_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="7b966362175f4e719aaf1a040615804d_3_1-choice_5-label" for="input_7b966362175f4e719aaf1a040615804d_3_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_7b966362175f4e719aaf1a040615804d_3_1"> Ability to synchronize the write field with the location of bits
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</div>
<span id="answer_7b966362175f4e719aaf1a040615804d_3_1"/>
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