Question 245: Magnetism and Matter

Question

Two concentric coils each of radius equal to $$2$$ $$\pi $$ $$cm$$ are placed at right  angles to each other. $$3$$ ampere and $$4$$ ampere  are the currents flowing in each coil respectively . The magnetic induction in Weber / $${m^2}$$ at the center of the coils will be 
$$\left( {\mu  = 4\pi  	imes {{10}^{ - 7}}Wb/A.m} ight)$$

Accepted Answer

The magnetic field due to circular coil $$1$$ and $$2$$ are
$${B_1} = {{{\mu _0}{i_1}} \over {2r}} = {{{\mu _0}{i_1}} \over {2\left( {2\pi  	imes {{10}^{ - 2}}} ight)}}$$
$$ = {{{\mu _0} 	imes 3 	imes {{10}^2}} \over {4\pi }}$$
$${B_2} = {{{\mu _0}{i_2}} \over {2\left( {2\pi  	imes {{10}^{ - 2}}} ight)}} = {{{\mu _0} 	imes 4 	imes {{10}^2}} \over {4\pi }}$$
$$B = \sqrt {B_1^2 + B_2^2}  = {{{\mu _0}} \over {4\pi }}.5 	imes {10^2}$$
$$ \Rightarrow B = {10^{ - 7}} 	imes 5 	imes {10^2}$$
$$ \Rightarrow B = 5 	imes {10^{ - 5}}\,Wb/{m^2}$$

Answer

$${10^{ - 5}}$$

Answer

$$12 	imes {10^{ - 5}}$$

Answer

$$7 	imes {10^{ - 5}}$$

Answer

$$5 	imes {10^{ - 5}}$$

Magnetism and Matter

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