<Text-field style="Heading 1" layout="Heading 1">Question 1</Text-field>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JSFHA conducting ring of radius LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is submerged in a spatially uniform magnetic field 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 field is perpendicular to the loop plain.What is the magnitude of the electromotive force inducted in the ring at a time LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHRfXzJgRictRiw2I1EhRic= ?
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>We will employ Lenz's law in order to find the emf. The magnetic flux through the loop is 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since the magnetic field is perpendicular to the loop plain. Using Lenz's law, the emf inducted in a loop is: 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print(); # input placeholder
JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 2</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0ZULyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUYsNiVRKmludGVyZmFjZUYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRLHR5cGVzZXR0aW5nRidGL0YyLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUYsNiVRKWV4dGVuZGVkRidGL0YyRjlGNQ==JSFHJSFHA system, as shown in the figure, is made of three metal rods, submerged in magnetic 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two perpendicular rods are static, and the third moves at a constant velocity LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, and forms a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEjNDVGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2Iy1JI21vR0YkNi1RKSZjb21wZm47RidGMi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjE2NjY2NjdlbUYnLyUncnNwYWNlR0ZMLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GODYtUSI6RidGMkY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjI3Nzc3NzhlbUYnL0ZORlY=print(); # input placeholderangle with the othe rods. At LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= this rod coincided the contact point between the two static rods. The spesific resistivity of the rods is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy .What is the inducted current in the rods after a time LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= ?
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>We will employ Lenz's law in order to find the emf. The area of the loop formed by the three rods is 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print(); # input placeholderand the magnetic flux through the loop is 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(); # input placeholdersince the magnetic field is perpendicular to the loop plain. Using Lenz's law, the emf inducted in a loop is: print(); # input 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print(); # input placeholderIn order to determine the current we have to know the total resistance of the rods. The perimiter of the loop at time t is 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print(); # input placeholderThe total resistance is 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print(); # input placeholderand, finally, the current is:
JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 3</Text-field>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A rod of length LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and resistance LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and mass LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is sliding down two conducting tracks. The tracks are straight, parallel, and inclined at an angle LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy relative to the horizon, and are connected to each other at the bottom. Also exists a constant uniform magnetic field LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= that points up, and a gravitational field LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= that points down.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LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlNUBGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiVnOEYqLSUpQ0hJTERSRU5HNiI=Find the rod's velocity at equilibrium.
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>Equilibrium is reached when the forces cancle each other 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print(); # input placeholderThe magnetic force's origin is the interaction between the induced current and the magnetic field.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(); # input placeholderWhere LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, the velocity of the rod is measured parallel to the tracks. The electromotive force is 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print(); # input placeholderand the current 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 = print(); # input placeholderThe interaction between this current and the magnetic field produces a force 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 = print(); # input placeholder that points up.Let us substitute it into the equilibrium equation, and isolate the velocity, and substitute the data given for the parameters:print(); # input placeholder
JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 4</Text-field>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A square loop of edge a and resistance LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is falling from hight LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= . A magnetic field LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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is perpendicular to the loop. Neglect the force on the loop due to the magnetic field. Find the current inside the loop when the loop meets the ground.
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>We will start by finding the magnetic flux through the loop as a function of the height. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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print(); # input placeholderNeglecting the force on the loop due to the magnetic field, we know y(t), substituting 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print(); # input placeholderand the current in the loop is 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 = print(); # input placeholderThe time required to the frame to fall is: 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 = print(); # input placeholderJSFHThe current in the loop when it reaches the ground:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=%;JSFHJSFH
<Text-field style="Heading 1" layout="Heading 1">Question 5</Text-field>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JSFHA conducting rod of length LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, mass LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and resistance LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is sliding on a horizontal track. At LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= the rod moves at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHZfXzBgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn past LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiT0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg==. The tracks are connected to each other at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiT0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg==. A constat uniform magnetic field LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= points down. Where will the rod stop?
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>The current in the rod is: PkknSV9fcm9kRzYiLCQqJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQqKEkiTEdGJCIiIkkiQkdGJEYtLUkieEdGJDYjSSJ0R0YkRi1GMkYtSSJSR0YkISIiRjQ=print(); # input placeholderThe force acting on the rod: PkkiRkc2IiooSSJMR0YkIiIiSSdJX19yb2RHRiRGJ0kiQkdGJEYnprint(); # input placeholderThe accseleration at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= is PkklYV9fMEc2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiQvLUklZGlmZkdGJzYkLUkieEdGJDYjSSJ0R0YkRjBJJXZfXzBHRiQqJkkiRkdGJCIiIkkibUdGJCEiIg==print(); # input placeholderWe will solve the equation of motion for the rod.print(); # input placeholderPkkkUG9zRzYiLUknZHNvbHZlR0YkNiM3Ji9JIkZHRiQqJkkibUdGJCIiIi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiUtSSJ4R0YkNiNJInRHRiRGNUY1Ri0vLUYzNiMiIiFGOS8tLUkiREc2JEYwSShfc3lzbGliR0YkNiNGM0Y4SSV2X18wR0YkLy0tRj02I0Y8RjhJJWFfXzBHRiQ=print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=