A 1 m long metal rod XY completes the circuit as shown in f igure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the circuit is 5ω, the force needed to move the rod in direction, as indicated, with a constant speed of 4 m/s will be ____10−3 N
Show Hint
Formulas for motional emf \((E = Blv)\) and the force on a current carrying conductor in a magnetic field \((F = BIl)\). Make sure your units are con sistent
Correct Answer: 18
Solution and Explanation
Step 1: Write the Force Equation
The force on a conductor in a magnetic field is given by:
\( F = I \ell B \)
Where:
- \( I \): Current
- \( \ell \): Length of the conductor in the magnetic field
- \( B \): Magnetic field strength
Step 2: Substitute \( I \) in Terms of \( e, R, \) and \( v \)
The current \( I \) can be expressed as:
\( I = \frac{e}{R} \)
Substitute \( I \) into the force equation:
\[ F = Bv \ell B \cdot \frac{\ell}{R} \]
Simplify:
\[ F = \frac{B^2 \ell^2 v}{R} \]
Step 3: Substitute Known Values
Given:
- \( B = 15 \, \text{T} \)
- \( \ell = 1 \, \text{m} \)
- \( v = 4 \, \text{m/s} \)
- \( R = 5 \, \Omega \)
Substitute these values into the equation:
\[ F = \frac{(15)^2 \cdot (1)^2 \cdot 4}{5} \]
Simplify:
\[ F = \frac{225 \cdot 4}{5} = 180 \, \text{N} \]
Final Answer:
The magnetic force is \( F = 18 \, \text{N}. \)
Top Questions on Magnetic Field
- Four long straight thin wires are held vertically at the corners A, B, C and D of a square of side \( a \), kept on a table and carry equal current \( I \). The wire at A carries current in upward direction whereas the current in the remaining wires flows in downward direction. The net magnetic field at the centre of the square will have the magnitude:
- CBSE CLASS XII - 2026
- Physics
- Magnetic Field
- A charged particle enters a magnetic field with velocity \( v \) at an angle of \( 60^\circ \) with the field. If the time period of the helical path is 2 seconds, the pitch of the helical path is:
- TS EAMCET - 2025
- Physics
- Magnetic Field
- Considering the case of magnetic field produced by air-filled current carrying solenoid, show that the magnetic energy density of a magnetic field \( B \) is \( \frac{B^2}{2\mu_0} \).
- CBSE CLASS XII - 2025
- Physics
- Magnetic Field
A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field \( B \) exists into the page. The bar starts to move from the vertex at time \( t = 0 \) with a constant velocity. If the induced EMF is \( E \propto t^n \), then the value of \( n \) is _____.
- JEE Main - 2025
- Physics
- Magnetic Field
- Read the following paragraph and answer the questions given below.
Ferromagnetic substances are those which get strongly magnetized when placed in an external magnetic field. They have strong tendency to move from a region of weak magnetic field to strong magnetic field, that is, they get strongly attracted to a magnet. The individual atoms (or ions or molecules) in a ferromagnetic material possess a dipole moment as in a paramagnetic material. However, they interact with one another in such a way that these spontaneously align themselves in a common direction over a macroscopic volume called domain. Each domain has a net magnetization. Typical domain size is 1 mm and the domain contains about \(10^{11}\) atoms. In the first instant the magnetization varies randomly from domain to domain and there is no bulk magnetization. When we apply an external magnetic field \(B_0\) the domains orient themselves in the direction of \(B_0\) and simultaneously that domain oriented in the direction of \(B_0\) grows in size. We may wonder as to what happens when the external field is removed, in some ferromagnetic materials the magnetization persists. Such materials are called hard magnetic materials of hard magnets. Alnico, an alloy of iron, aluminium, nickel, cobalt and copper is one such material. There is a class of magnetic materials in which the magnetization disappears on removal of the external field. Soft iron is one such material. Such materials are called soft ferromagnetic materials. There are number of elements which are ferromagnetic. Iron, cobalt, Nickel, gadolinium etc. The ferromagnetic property depends on temperature. At high enough temperature a ferromagnet becomes a paramagnet. That domain structure disintegrates with temperature. This disappearance of magnetization with the temperature is gradual.- PSEB XII - 2025
- Physics
- Magnetic Field
Questions Asked in JEE Main exam
A thin uniform rod (\(X\)) of mass \(M\) and length \(L\) is pivoted at a height \( \left(\dfrac{L}{3}\right) \) as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top is ________. (\(g\) = gravitational acceleration)
- JEE Main - 2026
- Rotational Mechanics
- In a microscope of tube length $10\,\text{cm}$ two convex lenses are arranged with focal lengths $2\,\text{cm}$ and $5\,\text{cm}$. Total magnification obtained with this system for normal adjustment is $(5)^k$. The value of $k$ is ___.
- JEE Main - 2026
- Optical Instruments
- Evaluate \[ \left(\frac{4}{7}+\frac{1}{3}\right)+\left(\frac{4}{7}+\frac{4}{3}\right)\left(\frac{1}{3}\right) +\left(\frac{4}{7}+\frac{4}{3}\right)^2\left(\frac{1}{3}\right)^2+\cdots \]
- JEE Main - 2026
- Arithmetic Progression
- The function \[ f(x)=\sin 2x+2\cos x,\qquad x\in\left(-\frac{3\pi}{4},\frac{3\pi}{4}\right) \] has:
If $\cot x=\dfrac{5}{12}$ for some $x\in(\pi,\tfrac{3\pi}{2})$, then \[ \sin 7x\left(\cos \frac{13x}{2}+\sin \frac{13x}{2}\right) +\cos 7x\left(\cos \frac{13x}{2}-\sin \frac{13x}{2}\right) \] is equal to
- JEE Main - 2026
- Trigonometric Identities