CBSE 2025 · Region 4 · Set 1 · Q23 · 3 marks
(a)Write vector form of Biot-Savart law.(b)Two insulated long straight wires, each carrying $\displaystyle 2 \cdot 0$ A current are kept along $\displaystyle \mathrm{xx}^{\prime}$ and $\displaystyle \mathrm{yy}^{\prime}$ axis as shown in the figure. Find the magnitude and direction of resultant magnetic field at point $\displaystyle \mathrm{P}(4 \mathrm{~m}, 5 \mathrm{~m})$.
(a)
Write vector form of Biot-Savart law.
(b)
Two insulated long straight wires, each carrying $\displaystyle 2 \cdot 0$ A current are kept along $\displaystyle \mathrm{xx}^{\prime}$ and $\displaystyle \mathrm{yy}^{\prime}$ axis as shown in the figure. Find the magnitude and direction of resultant magnetic field at point $\displaystyle \mathrm{P}(4 \mathrm{~m}, 5 \mathrm{~m})$.
Marking-scheme solution
(a)
$\displaystyle d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I(d \vec{l} \times \vec{r})}{r^{3}}$
(b)
As $\displaystyle B=\frac{\mu_{0}}{4 \pi} \frac{2 I}{a}$
$\displaystyle \vec{B}_{1}=$ Magnetic field due to current carrying wire along $\displaystyle XX^{\prime}$
$\displaystyle \vec{B}_{1}=\frac{\mu_{0}}{4 \pi} \frac{2 I}{a}=\frac{2 \times 2 \times 10^{-7}}{5}=\left(8 \times 10^{-8} \mathrm{~T}\right)(\hat{k})$
$\displaystyle \vec{B}_{2}=$ Magnetic field due to current carrying wire along $\displaystyle YY^{\prime}$
$\displaystyle \vec{B}_{2}=\frac{\mu_{0}}{4 \pi} \frac{2 I}{a}=\frac{2 \times 2 \times 10^{-7}}{4}=10 \times 10^{-8} \mathrm{~T}(-\hat{k})$
$\displaystyle \vec{B}_{\text {net }}=\vec{B}_{2}+\vec{B}_{1}$
$\displaystyle =2 \times 10^{-8} \mathrm{~T}(-\hat{k})$
Direction of resultant magnetic field along $\displaystyle -Z$ axis.
Moving Charges and MagnetismMagnetic Field due to a Current Element, Biot-Savart LawApplyshort_answermedium
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 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.