Two like magnetic poles of strength 10 and 40 | vedclass

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Question

(B) Let the magnetic field be zero at point $P$,which lies at a distance $x$ from the $10$ unit pole.Since the poles are like,the null point lies betw

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At a point $20 \, cm$ from the stronger pole

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(B) Let the magnetic field be zero at point $P$,which lies at a distance $x$ from the $10$ unit pole.Since the poles are like,the null point lies between them.The distance of $P$ from the $40$ unit pole is $(30 - x)$.At point $P$,the magnetic field intensities due to both poles must be equal in magnitude and opposite in direction:$\frac{\mu_0}{4\pi} \cdot \frac{10}{x^2} = \frac{\mu_0}{4\pi} \cdot \frac{40}{(30 - x)^2}$$\frac{1}{x^2} = \frac{4}{(30 - x)^2}$Taking the square root on both sides:$\frac{1}{x} = \frac{2}{30 - x}$$30 - x = 2x$$3x = 30 \Rightarrow x = 10 \, cm$.Thus,the point is at a distance of $10 \, cm$ from the $10$ unit pole and $(30 - 10) = 20 \, cm$ from the stronger ($40$ unit) pole.Therefore,the correct option is $(b)$.

Two like magnetic poles of strength $10$ and $40$ $SI$ units are separated by a distance of $30 \, cm$. The intensity of the magnetic field is zero on the line joining them at:

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