Question:
Two circular coils A and B are made from same wire but the radius of coil A is twice that of coil B. If the magnetic field at their centres is same then the ratio potential difference applied across them is
Two circular coils A and B are made from same wire but the radius of coil A is twice that of coil B. If the magnetic field at their centres is same then the ratio potential difference applied across them is
Show Hint
Write the field at the centre in terms of the current and radius, use the resistance proportional to length to relate current to voltage, and equate the two fields.
Updated On: Nov 12, 2026
- \(3:1\)
- \(4:1\)
- \(6:1\)
- \(2:1\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
The field at the centre of a circular coil is \(B=\frac{\mu_{0}I}{2r}\). The resistance of the same wire is proportional to its length, so \(R\propto r\).
Step 2: Current in Terms of Voltage
\(I=\frac{V}{R}\propto\frac{V}{r}\), so \(B\propto\frac{V}{r\cdot r}=\frac{V}{r^{2}}\).
Step 3: Equal Fields
\(\frac{V_{A}}{r_{A}^{2}}=\frac{V_{B}}{r_{B}^{2}}\).
Step 4: Calculation
\(\frac{V_{A}}{V_{B}}=\left(\frac{r_{A}}{r_{B}}\right)^{2}=2^{2}=4\).
Final Answer:
The potential differences are in the ratio 4 to 1. \[ \boxed{\text{(B) }4:1} \]
The field at the centre of a circular coil is \(B=\frac{\mu_{0}I}{2r}\). The resistance of the same wire is proportional to its length, so \(R\propto r\).
Step 2: Current in Terms of Voltage
\(I=\frac{V}{R}\propto\frac{V}{r}\), so \(B\propto\frac{V}{r\cdot r}=\frac{V}{r^{2}}\).
Step 3: Equal Fields
\(\frac{V_{A}}{r_{A}^{2}}=\frac{V_{B}}{r_{B}^{2}}\).
Step 4: Calculation
\(\frac{V_{A}}{V_{B}}=\left(\frac{r_{A}}{r_{B}}\right)^{2}=2^{2}=4\).
Final Answer:
The potential differences are in the ratio 4 to 1. \[ \boxed{\text{(B) }4:1} \]
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