Question:
A loop moves towards a stationary magnet at constant speed \(V\), resulting in an induced emf \(E\) within the loop. If the magnet also moves away from the loop at the same speed \(V\), the new induced emf in the loop is
A loop moves towards a stationary magnet at constant speed \(V\), resulting in an induced emf \(E\) within the loop. If the magnet also moves away from the loop at the same speed \(V\), the new induced emf in the loop is
Show Hint
Induced emf depends on the rate of change of magnetic flux, not on the individual motions of the magnet or loop.
If the relative position between the magnet and loop remains unchanged,
\[
\frac{d\Phi}{dt}=0
\]
and hence no emf is induced.
Updated On: Jul 9, 2026
- \(E\)
- \(\dfrac{E}{2}\)
- \(2E\)
- \(0\) \bigskip
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
According to Faraday's law,
\[
\mathcal{E}
=
-\frac{d\Phi}{dt},
\]
where \(\Phi\) is the magnetic flux linked with the loop.
An induced emf is produced only when the magnetic flux through the loop changes with time.
Step 1: Consider the initial situation. When the loop moves towards the stationary magnet with speed \(V\), \[ \frac{d\Phi}{dt}\neq 0. \] Hence an induced emf \[ \mathcal{E}=E \] is produced.
Step 2: Consider the new situation. Now the loop moves towards the magnet with speed \(V\), while the magnet simultaneously moves away from the loop with speed \(V\). Therefore, the relative speed between the loop and the magnet is \[ V-V=0. \] Hence the separation between them remains constant.
Step 3: Determine the change in magnetic flux. Since the distance between the loop and the magnet does not change, \[ \Phi=\text{constant}. \] Thus, \[ \frac{d\Phi}{dt}=0. \] Therefore, \[ \mathcal{E} = -\frac{d\Phi}{dt} = 0. \]
Step 4: Write the final answer. \[ \boxed{\mathcal{E}=0} \] \[ \boxed{\text{Answer = (D)}} \]
Step 1: Consider the initial situation. When the loop moves towards the stationary magnet with speed \(V\), \[ \frac{d\Phi}{dt}\neq 0. \] Hence an induced emf \[ \mathcal{E}=E \] is produced.
Step 2: Consider the new situation. Now the loop moves towards the magnet with speed \(V\), while the magnet simultaneously moves away from the loop with speed \(V\). Therefore, the relative speed between the loop and the magnet is \[ V-V=0. \] Hence the separation between them remains constant.
Step 3: Determine the change in magnetic flux. Since the distance between the loop and the magnet does not change, \[ \Phi=\text{constant}. \] Thus, \[ \frac{d\Phi}{dt}=0. \] Therefore, \[ \mathcal{E} = -\frac{d\Phi}{dt} = 0. \]
Step 4: Write the final answer. \[ \boxed{\mathcal{E}=0} \] \[ \boxed{\text{Answer = (D)}} \]
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Electromagnetic induction Questions
- What does Lenz's Law give ?
- When two coaxial coils having the same current in the same direction are brought close to each other, then the value of current in both the coils:
- The ratio of the flux-linkage to current is
- A changing current in a coil can induce an emf in a nearby coil. This process is:
- An ac generator converts
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions