(ii) Almost all symbols (whether Latin or Greek) should be typed in italics. The three main exceptions are mathematical functions (cos, ln, subscripts that relate to etc.), names or words (kB, and physical units (mA, kg, Vectors should be Eext, etc.), etc.). normally be typed in (without arrow or underline). Subscripts and bold italic superscripts should be 9-point size. Type 0 (i.e. zero), not o (i.e. the for letter ‘oh’), superscript or a space between quantity and unit, and subscript ‘nought’. Put between elements of a unit (e.g. 59 m s–1, 59ms–1). Do not use a as not hyphen (‘-’) a minus sign, the is longer. correct symbol (‘–’) Punctuate formulae and symbols as [9] parts of the sentence that contains them. 3. Define the vector potential and state how it is related to the A long thin wire, length in free space carries a current Provided the magnitude L, I. of the vector potential at a distance from the midpoint of the wire on a line A r perpendicular to its axis is (a) What is the direction of the vector [2] A? (b) Use the the vector potential to find an expression for the magnetic flux density due to the wire. [4] B Hence find the flux through the square loop (which lies in the same plane as the wire) shown in the diagram. [5] If the loop has a resistance and the current flowing in the straight wire increases at I a rate of 3 A s–1 what current is induced in the loop if its area is 5 cm2 ? Ignore the self-inductance of the loop, ignore the field due to induced currents circulating. i.e. Under what circumstances would you expect this to be a poor approximation? [4] Turn Over
(ii) Almost all symbols (whether Latin or Greek) should be typed in italics. The three main exceptions are mathematical functions (cos, ln, etc.), subscripts that relate to names or words (kB, Eext, etc.), and physical units (mA, kg, etc.). Vectors should be normally be typed in bold italic (without arrow or underline). Subscripts and superscripts should be 9-point size. Type 0 (i.e. zero), not o (i.e. the letter ‘oh’), for superscript or subscript ‘nought’. Put a space between quantity and unit, and between elements of a unit (e.g. 59 m s–1, not 59ms–1). Do not use a hyphen (‘-’) as a minus sign, the correct symbol (‘–’) is longer. Punctuate formulae and symbols as parts of the sentence that contains them. [9] Turn Over 3. Define the vector potential and state how it is related to the A long thin wire, length L, in free space carries a current I. Provided the magnitude of the vector potential A at a distance r from the midpoint of the wire on a line perpendicular to its axis is (a) What is the direction of the vector A? [2] (b) Use the the vector potential to find an expression for the magnetic flux density B due to the wire. [4] Hence find the flux through the square loop (which lies in the same plane as the wire) shown in the diagram. [5] If the loop has a resistance and the current I flowing in the straight wire increases at a rate of 3 A s–1 what current is induced in the loop if its area is 5 cm2 ? Ignore the self-inductance of the loop, i.e. ignore the field due to induced currents circulating. Under what circumstances would you expect this to be a poor approximation? [4]
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