<Text-field style="Heading 1" layout="Heading 1">Question 1 & 2</Text-field>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A frame carring current LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is placed near an infinite wire carring a current LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= . 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LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlXUVGKi0lLkJPVU5EU19IRUlHSFRHRi8tJSlDSElMRFJFTkc2Ig==What is the magnitude of the force acting on the adge LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjQkNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn due to the magnetic field of the infinite wire?
<Text-field style="Heading 2" layout="Heading 2">Solution for 1</Text-field>Let us use Ampere's law to determine the magnetic field of the infinite wire: 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 = print(); # input placeholderSince the magnetic field is perpenticular to the frame plain, the magnetic force acting on LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjQkNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn becomes 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print(); # input placeholder
What is the magnitude of the force acting on the edge LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjQUZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn due to the wire's magnetic field?LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Solution for 2</Text-field>In this case, only the length of the wire and the current's direction have been changed. We are interested in the magnitude, so the current's direction is not important.All we have to do is change the points: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EnYEZfXzJgRictSSNtb0dGJDYtUSomY29sb25lcTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1GLDYlUSVzdWJzRicvJSdpdGFsaWNHUSV0cnVlRicvRjRRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRlM2Ji1GIzYpLUYsNiVRImJGJ0ZNRlAtRjA2LVEiPUYnRjNGNkY5RjtGPUY/RkFGQ0ZFRkgtRiw2JVEiYUYnRk1GUC1GMDYtUSIsRidGM0Y2L0Y6Rk9GO0Y9Rj9GQUZDL0ZGUSYwLjBlbUYnL0ZJUSwwLjMzMzMzMzNlbUYnLUYsNiVRImNGJ0ZNRlBGaG4tRiw2JVEiZkYnRk1GUEYzLyUlb3BlbkdRInxmckYnLyUmY2xvc2VHUSJ8aHJGJ0Zeby1GLDYlUSJGRidGTUZQRjMtRjA2LVEiOkYnRjNGNkY5RjtGPUY/RkFGQ0ZFRkg=print(); # input placeholder
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 3</Text-field>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 long wire of circular cross-section of radius 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 is carring a uniform current 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What is the magnitic field magnitude at distance 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from the wire's axis?
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>Using Ampere's law, we deduce that only the current flowing at 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contributs to the magnetic field at 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We write the current as an integral of the current density on the circle of radius LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= . LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 4</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0ZULyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUYsNiVRKmludGVyZmFjZUYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRLHR5cGVzZXR0aW5nRidGL0YyLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUYsNiVRKWV4dGVuZGVkRidGL0YyRjlGNS1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIL0ZLRlcvRk5GV0ZPLUZQNiZGUkZVRlgvRmVuUSVhdXRvRictRiw2JVEld2l0aEYnRi9GMi1GW282JC1GIzYjLUYsNiVRNFNjaWVudGlmaWNDb25zdGFudHNGJ0YvRjJGOUY1JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=A rectangular loop (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) lies in the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjeHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn plain, and carries a current of 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What is the magnetic field magnitude at hight of 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above the center of the loop?JSFH
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>In order to find the total magnetic field, we will determine the magnetic field produced by a finite wire of length LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, at a distance LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= from its middle using Biot-Savart law.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 = print(); # input placeholderWhere 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 is a unit vector, and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the distance from the wire.The total field is composed of the contributions of all the edges.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(); # input placeholderIn the last substituition, instead of writing the vector sum of the four edges, we substituted only the vertical component of the unit vector.print(); # input placeholder
JSFHJSFH
<Text-field style="Heading 1" layout="Heading 1">Question 5 & 6 </Text-field>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 particle of mass QyQvSSJtRzYiLCRJI01wR0YlIiNDISIi and a charge of QyQvSSJxRzYiLCRJImVHRiUiIiYhIiI= is moving prependiculary to a magnetic field QyQvSSJCRzYiLUklVW5pdEdGJTYjLkkiVEdGJSEiIg==What is its angular velocity LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy ?print(); # input placeholder
<Text-field style="Heading 2" layout="Heading 2">Solution for 5</Text-field>The force acting on the particle due to the magnetic field must be the centripital force: QyQ+SSRlcTFHNiIvKihJIm1HRiUiIiJJJm9tZWdhR0YlIiIjSSJyR0YlRikqKEkicUdGJUYpSSJ2R0YlRilJIkJHRiVGKSEiIg==print(); # input placeholdersince the linear velocity and the angular velocity are related by QyQ+SSRlcTJHNiIvKiZJInJHRiUiIiJJJm9tZWdhR0YlRilJInZHRiUhIiI=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=print(); # input placeholder
What is the radius of the trajectory of the particle if its velovity is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRJTAuMDFGJ0Y5LUY2Ni1RJyZzZG90O0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZXLUYsNiVRImNGJ0YvRjJGOQ== ? LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the speed of light.
<Text-field style="Heading 2" layout="Heading 2">Solution for 6</Text-field>The answer is clear from eq2: