Source And Effects Of Magnetic Field | Physics JEE previous year questions with Solutions

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Topic Question Set

Q 1 :
Two insulated circular loops A and B of radius 'a' carrying a current of 'I' in the anti-clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be ______. [2024]

$\frac{\sqrt{2} μ_{0} I}{2 a}$
$\frac{μ_{0} I}{2 a}$
$\frac{\sqrt{2} μ_{0} I}{a}$
$\frac{2 μ_{0} I}{a}$

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(1)

${\vec{B}}_{A} = \frac{μ_{0} I}{2 a}$

${\vec{B}}_{B} = \frac{μ_{0} I}{2 a}$ $∵$ ${\vec{B}}_{net} = \frac{\sqrt{2} μ_{0} I}{2 a}$

Q 2 :
The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $R_{1} = 2 π m$ and $R_{2} = 4 π m$ , carrying current $I = 4 A$ as per figure given below is $α \times 10^{- 7} T$ . The value of $α$ is ______. (Centre O is common for all segments) [2024]

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(3)

$\frac{μ_{0} i}{2 R_{2}} (\frac{π}{2 π}) \otimes + \frac{μ_{0} i}{2 R_{1}} (\frac{π}{2 π}) \otimes$

$(\frac{μ_{0} i}{4 R_{2}} + \frac{μ_{0} i}{4 R_{1}}) \otimes$

$\frac{4 π \times 10^{- 7} \times 4}{4 \times 4 π} + \frac{4 π \times 10^{- 7} \times 4}{4 \times 2 π}$

$= 3 \times 10^{- 7} = α \times 10^{- 7}$

$α = 3$

Q 3 :
Two circular coils P and Q of 100 turns each have same radius of $π$ cm. The currents in P and R are 1A and 2A respectively. P and Q are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $\sqrt{x} m T,$ where $x =$ ____ .

$[Use μ_{0} = 4 π \times 10^{- 7} {TmA}^{- 1}]$ [2024]

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(20)

$B_{P} = \frac{μ_{0} N i_{1}}{2 r} = \frac{μ_{0} \times 1 \times 100}{2 π} = 2 \times 10^{- 3} T$

$B_{Q} = \frac{μ_{0} N i_{2}}{2 r} = \frac{μ_{0} \times 2 \times 100}{2 π} = 4 \times 10^{- 3} T$

$B_{net} = \sqrt{B_{P}^{2} + B_{Q}^{2}} = \sqrt{20} mT$

$x = 20$

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