TEST

profrsmurthy — Thu, 13 Mar 2008 13:36:51 +0000

' title='' class='latex' />
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$$
\eqalign{
& B = \frac{{\mu _o }}
{{4\pi }}\sqrt {3\cos ^2 \theta + 1} \cr
& \therefore 3.75 \times 10^{ – 5} = 10^{ – 7} \frac{M}
{{(0.2)^3 }}\sqrt {3\cos ^2 60 + 1} \cr
& \therefore M = 2.268\,Am^2 \cr
& \therefore m \times 2\ell = 2.268\therefore m \times 0.02 = 2.268 \cr
& \therefore m = 113.4\,Am \cr}
$$
% MathType!End!2!1!

TEST

profrsmurthy — Thu, 13 Mar 2008 13:33:02 +0000

[2] Determine the magnetic induction and magnetic potential due to a short magnetic dipole of moment 5 % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!% MathType!MTEF!2!1!+-% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaiabgk% HiTiaad2gadaahaaWcbeqaaiaaikdaaaaaaa!397B!\[A - m^2 \]% MathType!End!2!1!at a distance of 100 cm from its centre along a line making an angle of 60% MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!% MathType!MTEF!2!1!+-% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaWbaaSqabe% aacaWGVbaaaaaa!370E!\[^o \]% MathType!End!2!1!

with its axis.

Solution : % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!% MathType!MTEF!2!1!+-% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiVd02aaS% baaSqaaiaad+gaaeqaaOGaeyypa0JaaGinaiabec8aWjabgEna0kaa% igdacaaIWaWaaWbaaSqabeaacqGHsislcaaI3aaaaOGaaGPaVlaadE% facaWGIbGaai4laiaadgeacqGHsislcaWGTbGaaiilaiaad2eacqGH% 9aqpcaaI1aGaamyqaiabgkHiTiaad2gadaahaaWcbeqaaiaaikdaaa% GccaGGSaGaamOCaiabg2da9iaaigdacaWGTbGaaiilaiabeI7aXjab% g2da9iaaiAdacaaIWaWaaWbaaSqabeaacaWGVbaaaaaa!59A5!\[\mu _o = 4\pi \times 10^{ - 7} \,Wb/A - m,M = 5A - m^2 ,r = 1m,\theta = 60^o \]% MathType!End!2!1! % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!% MathType!MTEF!2!1!+-% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGcb% Gaeyypa0ZaaSaaaeaacqaH8oqBdaWgaaWcbaGaam4Baaqabaaakeaa% caaI0aGaeqiWdahaaiabgEna0oaalaaabaGaamytaaqaaiaadkhada% ahaaWcbeqaaiaaiodaaaaaaOWaaOaaaeaacaaIZaGaci4yaiaac+ga% caGGZbWaaWbaaSqabeaacaaIYaaaaOGaeqiUdeNaey4kaSIaaGymaa% Wcbeaakiabg2da9iaaigdacaaIWaWaaWbaaSqabeaacqGHsislcaaI% 3aaaaOGaey41aq7aaSaaaeaacaaI1aaabaGaaiikaiaaigdacaGGPa% WaaWbaaSqabeaacaaIZaaaaaaakmaakaaabaGaaG4maiGacogacaGG% VbGaai4CamaaCaaaleqabaGaaGOmaaaakiaaiAdacaaIWaGaey4kaS% IaaGymaaWcbeaakiabg2da9iaaiwdadaGcaaqaaiaaiodacqGHxdaT% daWcaaqaaiaaigdaaeaacaaI0aaaaiabgUcaRiaaigdaaSqabaGccq% GH9aqpdaWcaaqaaiaaiwdaaeaacaaIYaaaamaakaaabaGaaGymaiaa% c6cacaaI3aGaaGynaaWcbeaaaOqaaiaaykW7caaMc8UaaGPaVlaayk% W7cqGH9aqpcaaIYaGaaiOlaiaaiwdadaGcaaqaaiaaiEdaaSqabaGc% cqGHxdaTcaaIXaGaaGimamaaCaaaleqabaGaeyOeI0IaaG4naaaaki% abg2da9iaaiAdacaGGUaGaaGOnaiaaigdacaaI1aGaaGPaVlabgEna% 0kaaigdacaaIWaWaaWbaaSqabeaacqGHsislcaaI3aaaaOGaam4vai% aadkgacaGGVaGaamyBamaaCaaaleqabaGaaGOmaaaaaaaa!8954!\[\begin{gathered} B = \frac{{\mu _o }}{{4\pi }} \times \frac{M}{{r^3 }}\sqrt {3\cos ^2 \theta + 1} = 10^{ - 7} \times \frac{5}{{(1)^3 }}\sqrt {3\cos ^2 60 + 1} = 5\sqrt {3 \times \frac{1}{4} + 1} = \frac{5}{2}\sqrt {1.75} \hfill \\ \,\,\,\, = 2.5\sqrt 7 \times 10^{ - 7} = 6.615\, \times 10^{ - 7} Wb/m^2 \hfill \\ \end{gathered} \]% MathType!End!2!1! % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!% MathType!MTEF!2!1!+-% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaaciGG0b% Gaaiyyaiaac6gacqaHXoqycqGH9aqpdaWcaaqaaiaaigdaaeaacaaI% YaaaaiGacshacaGGHbGaaiOBaiaaiAdacaaIWaGaeyypa0ZaaSaaae% aacaaIXaaabaGaaGOmaaaacaGGOaGaaGymaiaac6cacaaI3aGaaG4m% aiaaikdacaGGPaGaeyypa0JaaGimaiaac6cacaaI4aGaaGOnaiaaiA% daaeaacqaHXoqycqGH9aqpciGG0bGaaiyyaiaac6gadaahaaWcbeqa% aiabgkHiTiaaigdaaaGccaGGOaGaaGimaiaac6cacaaI4aGaaGOnai% aaiAdacaGGPaGaeyypa0JaaGinaiaaicdadaahaaWcbeqaaiaad+ga% aaGccaaI1aGaaGinaiaacEcaaaaa!5FAA!\[\begin{gathered} \tan \alpha = \frac{1}{2}\tan 60 = \frac{1}{2}(1.732) = 0.866 \hfill \\ \alpha = \tan ^{ - 1} (0.866) = 40^o 54' \hfill \\ \end{gathered} \]% MathType!End!2!1! % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!% MathType!MTEF!2!1!+-% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvaiabg2% da9maalaaabaGaeqiVd02aaSbaaSqaaiaad+gaaeqaaaGcbaGaaGin% aiabec8aWbaadaWcaaqaaiaad2eaciGGJbGaai4BaiaacohacqaH4o% qCaeaacaWGYbWaaWbaaSqabeaacaaIYaaaaaaakiabg2da9iaaigda% caaIWaWaaWbaaSqabeaacqGHsislcaaI3aaaaOGaey41aq7aaSaaae% aacaaI1aGaci4yaiaac+gacaGGZbGaaGOnaiaaicdaaeaacaGGOaGa% aGymaiaacMcadaahaaWcbeqaaiaaikdaaaaaaOGaeyypa0JaaGymai% aaicdadaahaaWcbeqaaiabgkHiTiaaiEdaaaGccqGHxdaTcaaI1aGa% ey41aq7aaSaaaeaacaaIXaaabaGaaGOmaaaacqGH9aqpcaaIYaGaai% OlaiaaiwdacqGHxdaTcaaIXaGaaGimamaaCaaaleqabaGaeyOeI0Ia% aG4naaaakiaadQeacaGGVaGaamyqaiaad2gaaaa!69DA!\[V = \frac{{\mu _o }}{{4\pi }}\frac{{M\cos \theta }}{{r^2 }} = 10^{ - 7} \times \frac{{5\cos 60}}{{(1)^2 }} = 10^{ - 7} \times 5 \times \frac{1}{2} = 2.5 \times 10^{ - 7} J/Am\]% MathType!End!2!1! ' title='[2] Determine the magnetic induction and magnetic potential due to a short magnetic dipole of moment 5 % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!% MathType!MTEF!2!1!+-% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaiabgk% HiTiaad2gadaahaaWcbeqaaiaaikdaaaaaaa!397B!\[A - m^2 \]% MathType!End!2!1!at a distance of 100 cm from its centre along a line making an angle of 60% MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!% MathType!MTEF!2!1!+-% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaWbaaSqabe% aacaWGVbaaaaaa!370E!\[^o \]% MathType!End!2!1!

with its axis.

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