Question:
Two parallel wires of equal lengths are separated by a distance of \(3\) m from each other. The currents flowing through first and second wire is \(3\) A and \(4.5\) A respectively in opposite directions. The resultant magnetic field at mid point of both the wires is (\(μ_0\)=permeability of free space)
Two parallel wires of equal lengths are separated by a distance of \(3\) m from each other. The currents flowing through first and second wire is \(3\) A and \(4.5\) A respectively in opposite directions. The resultant magnetic field at mid point of both the wires is (\(μ_0\)=permeability of free space)
Show Hint
At the midpoint, fields of opposite currents point the same way and add.
Updated On: Oct 1, 2026
- \(\frac{μ_0}{2π}\)
- \(\frac{5μ_0}{2π}\)
- \(\frac{7μ_0}{2π}\)
- \(\frac{9μ_0}{2π}\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
A long straight wire gives \(B=\dfrac{\mu_0I}{2\pi r}\) at distance \(r\). For two parallel wires with opposite currents, the fields between the wires point in the same direction.
Step 2: Find the distances and fields:
The midpoint is \(1.5\) m from each wire. \(B_1=\dfrac{\mu_0(3)}{2\pi(1.5)}=\dfrac{2\mu_0}{2\pi}\). \(B_2=\dfrac{\mu_0(4.5)}{2\pi(1.5)}=\dfrac{3\mu_0}{2\pi}\).
Step 3: Add them:
\(B=B_1+B_2=\dfrac{2\mu_0}{2\pi}+\dfrac{3\mu_0}{2\pi}=\dfrac{5\mu_0}{2\pi}\). Option B.
Step 4: Why the other options are wrong.
\(\dfrac{\mu_0}{2\pi}\) is the difference of the two fields, which holds for currents in the same direction. 7 and 9 come from using the wrong distance.
Final Answer:
The magnetic field is 5 mu0 / (2 pi). \[ \boxed{\text{(B) }\dfrac{5\mu_0}{2\pi}} \]
A long straight wire gives \(B=\dfrac{\mu_0I}{2\pi r}\) at distance \(r\). For two parallel wires with opposite currents, the fields between the wires point in the same direction.
Step 2: Find the distances and fields:
The midpoint is \(1.5\) m from each wire. \(B_1=\dfrac{\mu_0(3)}{2\pi(1.5)}=\dfrac{2\mu_0}{2\pi}\). \(B_2=\dfrac{\mu_0(4.5)}{2\pi(1.5)}=\dfrac{3\mu_0}{2\pi}\).
Step 3: Add them:
\(B=B_1+B_2=\dfrac{2\mu_0}{2\pi}+\dfrac{3\mu_0}{2\pi}=\dfrac{5\mu_0}{2\pi}\). Option B.
Step 4: Why the other options are wrong.
\(\dfrac{\mu_0}{2\pi}\) is the difference of the two fields, which holds for currents in the same direction. 7 and 9 come from using the wrong distance.
Final Answer:
The magnetic field is 5 mu0 / (2 pi). \[ \boxed{\text{(B) }\dfrac{5\mu_0}{2\pi}} \]
Was this answer helpful?
0
0
Top MHT CET Physics Questions
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- A particle moves along a circle of radius ?$r$? with constant tangential acceleration. If the velocity of the particle is ?$?$? at the end of second revolution, after the revolution has started then the tangential acceleration is
- If $M_z$ = magnetization of a paramagnetic sample, $B$ = external magnetic field, $T$ = absolute temperature, $C$ = curie constant then according to Curie�s law in magnetism, the correct relation is
- In a fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with air is $'t'$ second. The frequency of vibration of air column is
- In a parallel plate capacitor, the capacity increases if
View More Questions
Top MHT CET Magnetic Field Questions
- The ratio of magnetic fields due to a bar magnet at the two axial points $P_1$ and $P_2$ which are separated from each other by $10 \,cm$ is 25 : 2. Point $P_1$ is situated at 10 cm from the centre of the magnet. Magnetic length of the bar magnet is (Points $P_1$ and $P_2$ are on the same side of magnet and distance of $P_2$ from the centre is greater than distance of $P_1$ from the centre of magnet)
- Which of the following while in motion cannot be deflected by magnetic field ?
A magnetic field is produced along the axis of a current-carrying loop. The direction and magnitude of the magnetic field at the center of the loop can be determined using the Biot-Savart law. What will be the direction of the magnetic field along the axis of the current loop? The magnetic field produced along the axis of a circular current loop is given by the equation: \[ B = \frac{{\mu_0 I R^2}}{{2 (R^2 + x^2)^{3/2}}} \]
where:
\( B \) is the magnetic field,
\( \mu_0 \) is the permeability of free space,
\( I \) is the current,
\( R \) is the radius of the loop,
\( x \) is the distance from the center of the loop along the axis.- A circular loop of radius 0.2 m carries a current of 4 A. What is the magnetic field at a point on the axis of the loop at a distance 0.2 m from the center?
- A coil of 100 turns, carrying a current of 5A, is placed in a magnetic field of 2T. The area of each turn is 0.01 m\(^2\). What is the magnetic moment of the coil?
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions