Magnetic Properties of Matter

JEE Main level, single correct, medium

20 of 57

Question 20 of 57

Two coils ′P′'P' and ′Q′'Q' are separated by some distance. When a current of 3A3A flows through coil ′P′,'{P}^{'}, a magnetic flux of 10−3Wb{10}^{-3}Wb passes through ′Q′.'{Q}^{'}. No current is passed through ′Q′.'{Q}^{'}. When no current passes through ′P′'P' and a current of 2A2A passes through ′Q′,'{Q}^{'}, the flux through ′P′'P' is:

Show answer and solution

Answer: (B) 6.67×10−4Wb6.67\times {10}^{-4} Wb

Since the coils are co-axial, the flux through the coils can be written as the product of their surface area and the magnetic field produced by the coil along its axis.
Consider the flux passing through Q
ϕQ=μ0i1R22(R2+x2)32×πR2=10−3Wb{\phi }_{Q}=\dfrac{{\text{μ}}_{0}{i}_{1}{R}^{2}}{2{\left({R}^{2}+{x}^{2}\right)}^{\dfrac{3}{2}}}\times \text{π}{R}^{2}={10}^{-3}Wb

And the flux passing through P:
ϕP=μ0i1r22(R2+x2)32×πR2{\phi }_{P}=\dfrac{{\text{μ}}_{0}{i}_{1}{r}^{2}}{2{\left({R}^{2}+{x}^{2}\right)}^{\dfrac{3}{2}}}\times \text{π}{R}^{2}
Taking the ratio
ϕPϕQ=i2i1×(R2+x2)32(R2+x2)32⇒ϕP10−3=i2i1\dfrac{{\phi }_{P}}{{\phi }_{Q}}=\dfrac{{i}_{2}}{{i}_{1}}\times \dfrac{{\left({R}^{2}+{x}^{2}\right)}^{\dfrac{3}{2}}}{{\left({R}^{2}+{x}^{2}\right)}^{\dfrac{3}{2}}}\Rightarrow \dfrac{{\phi }_{P}}{{10}^{-3}}=\dfrac{{i}_{2}}{{i}_{1}}
⇒ϕP10−3=23\Rightarrow \dfrac{{\phi }_{P}}{{10}^{-3}}=\dfrac{2}{3}
∴ϕP=6.67×10−4Wb∴{\phi }_{P}=6.67\times {10}^{-4} Wb

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.

More Physics practice

JEE Main Physics practice question on Magnetic Properties of Matter (Magnetism and Properties of Magnet), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.