CBSE 2026 · Region 4 · Set 1 · Q23 · 3 marks
The figure given below shows three straight long parallel conductors ($\displaystyle 1$), ($\displaystyle 2$) and ($\displaystyle 3$) kept in x-y plane, carrying currents 2I, I and 3I respectively as shown in figure.
Find the magnitude and direction of :(i)net magnetic field at a point on conductor ($\displaystyle 1$) and(ii)net magnetic force acting on unit length of conductor ($\displaystyle 1$), due to conductors ($\displaystyle 2$) and ($\displaystyle 3$).A rectangular loop of sides $\displaystyle l$ and b and resistance 'R' is kept in a region in which the magnetic field varies as $\displaystyle \mathrm{B}=\mathrm{B}_{0} \sin \omega \mathrm{t}$.(i)Derive expression for the emf induced in the loop.(ii)Find the effective value of current that flows in the loop.
The figure given below shows three straight long parallel conductors ($\displaystyle 1$), ($\displaystyle 2$) and ($\displaystyle 3$) kept in x-y plane, carrying currents 2I, I and 3I respectively as shown in figure.
Find the magnitude and direction of :
(i)
net magnetic field at a point on conductor ($\displaystyle 1$) and
(ii)
net magnetic force acting on unit length of conductor ($\displaystyle 1$), due to conductors ($\displaystyle 2$) and ($\displaystyle 3$).
A rectangular loop of sides $\displaystyle l$ and b and resistance 'R' is kept in a region in which the magnetic field varies as $\displaystyle \mathrm{B}=\mathrm{B}_{0} \sin \omega \mathrm{t}$.
(i)
Derive expression for the emf induced in the loop.
(ii)
Find the effective value of current that flows in the loop.
Marking-scheme solution
Finding the magnitude and direction of:
(i)
Magnetic field due to conductor ($\displaystyle 2$) at a point on conductor ($\displaystyle 1$) is $\displaystyle \mathrm{B}_{1}=\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{~d}}$ along positive z - axis.
Magnetic field due to conductor ($\displaystyle 3$) at a point on conductor ($\displaystyle 1$) is $\displaystyle \mathrm{B}_{2}=\frac{3 \mu_{0} \mathrm{I}}{4 \pi \mathrm{~d}}$ along negative z - axis.
Magnitude of net magnetic field is $\displaystyle \mathrm{B}_{2}-\mathrm{B}_{1}=\frac{3 \mu_{0} \mathrm{I}}{4 \pi \mathrm{d}}-\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{d}}=\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{d}}$ along negative $\displaystyle z-$ axis.
Direction will be along negative z axis/ into the plane of the paper.
(ii)
Force per unit length on conductor ($\displaystyle 1$) due to conductor ($\displaystyle 2$) $\displaystyle =\frac{\mu_{0} \mathrm{I}_{1} \mathrm{I}_{2}}{2 \pi \mathrm{~d}}$
\[=\frac{\mu_{0} \mathrm{I}^{2}}{\pi \mathrm{~d}} \text { (attractive) }
\]
Force per unit length on conductor ($\displaystyle 1$) due to conductor ($\displaystyle 3$) $\displaystyle =\frac{3 \mu_{0} \mathrm{I}^{2}}{2 \pi \mathrm{~d}}$ (repulsive)
Magnitude of net force per unit length on conductor ($\displaystyle 1$) due to ($\displaystyle 2$) & ($\displaystyle 3$) $\displaystyle =\frac{\mu_{0} \mathrm{I}^{2}}{2 \pi \mathrm{~d}}$
Direction of the net force per unit length will be repulsive or along positive $\displaystyle y$-axis.
(b)
Deriving expression for induced emf
(ii)
Finding the effective value of current
\[\begin{aligned}
\text { Induced emf } & =|\varepsilon|=\frac{\mathrm{d} \phi}{\mathrm{dt}} \\
& =\frac{\mathrm{d}}{\mathrm{dt}}(\overrightarrow{\mathrm{~B}} \cdot \overrightarrow{\mathrm{~A}})
\end{aligned}
\]
Moving Charges and MagnetismForce between Two Parallel Currents, the AmpereApplyshort_answerhard
More from Moving Charges and Magnetism
- A 2.0 cm segment of wire, carrying 5.0 A current in positive y-direction lies along y -axis, as shown in the…2024 · asked 3×
- Derive an expression for the magnetic field B, due to a circular coil of N turns, each of radius r carrying…2026 · asked 3×
- Assertion: A proton and an electron enter a uniform magnetic field B with the same momentum p such that p is…2024 · asked 3×
- (i) A particle of mass m and charge q is moving with a velocity v in a magnetic field B as shown in the…2024 · asked 3×
- Figure shows a narrow beam of electrons entering with a velocity of 3 × 10^7 m / s, symmetrically through the…2026 · asked 3×
- A 1 cm straight segment of a conductor carrying 1 A current in x direction lies symmetrically at origin of…2025 · asked 3×
- A rectangular loop carries a current of 1 A. A straight long wire carrying 2 A current is kept near the loop…2025 · asked 3×
- Assertion: Two long parallel wires, freely suspended and connected in series to a battery, move apart. Reason…2024 · asked 3×
CBSE Class 12 Physics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.