eSaral - JEE | NEET | Class 8-10 Exam Prep App

A long, straight wire of radius r carries a current i and

Question: A long, straight wire of radius $r$ carries a current $i$ and placed horizontally in a uniform magnetic field B pointing vertically upward. The current is uniformly distributed over its cross-section. (a) At what points will the resultant magnetic field have maximum magnitude? (b) What will be the minimum magnitude of the resultant magnetic field? Solution:...

A long, straight wire carrying a current of

Question: A long, straight wire carrying a current of $1.0 \mathrm{~A}$ is placed horizontally in a uniform magnetic field $\mathrm{B}=1.0 \times 10^{-5} \mathrm{~T}$ pointing vertically upward. Find the magnitude of the resultant magnetic field at the points $P$ and $Q$, both situated at a distance of $2.0 \mathrm{~cm}$ from the wire in the same horizontal plane. Solution:...

A transmission wire carries a current of 100A.

Question: A transmission wire carries a current of $100 \mathrm{~A}$. What would be the magnetic field $B$ at a point on the road if the wire is $8 \mathrm{~m}$ above the road? Solution:...

A copper wire of diameter 1.6mm carries a current of 20A.

Question: A copper wire of diameter $1.6 \mathrm{~mm}$ carries a current of $20 \mathrm{~A}$. Find the maximum magnitude of the magnetic field $\vec{B}$ due to this current. Solution:...

A current of 10A is established in a long wire along the positive Z-axis.

Question: A current of $10 \mathrm{~A}$ is established in a long wire along the positive Z-axis. Find the magnetic field $\overrightarrow{\mathrm{B}}$ at the point $(1 \mathrm{~m}, 0,0)$. Solution:...

Using the formulae

Question: Using the formulae $\overrightarrow{\mathrm{F}}=\mathrm{qv} \times \overrightarrow{\mathrm{B}}$ and $\mathrm{B}=\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{r}}$ show that the $\mathrm{SI}$ units of the magnetic field $B$ and the permeability constant $\mu_{0}$ may be written as $N / A-m$ and $N / A^{2}$ respectively. Solution:...

The rate of working of an engine is given by.

Question: The rate of working of an engine is given by. $R=15 v+\frac{6000}{v}$, where $0v30$ and $v$ is the speed of the engine. Show that $R$ is the least when $v=20$. Solution:...

Divide a into two parts such that the product of

Question: Divide a into two parts such that the product of the pth power of one part and the qth power of the second part may be maximum. Solution: $=x^{p-1}(a-x)^{q-1}[a p-x p-x q]$...

Consider a solid sphere of radius r and mass m

Question: Consider a solid sphere of radius $\mathrm{r}$ and mass $\mathrm{m}$ which has a charge $\mathrm{q}$ distributed uniformly over its volume. The sphere is rotated about a diameter with an angular speed $\omega$. Show that the magnetic moment $\mu$ and the angular momentum I of the sphere are related as $\mu=\frac{q}{2 m} l$. Solution:...

Divide 8 into two positive parts such that the sum of the square of one and the cube of the other is minimum.

Question: Divide 8 into two positive parts such that the sum of the square of one and the cube of the other is minimum. Solution:...

Consider a nonconducting plate of radius r and

Question: Consider a nonconducting plate of radius $r$ and mass $m$ which has a charge $q$ distributed uniformly over it. The plate is rotated about its axis with an angular speed $\omega$. Show that the magnetic moment $\mu$ and the angular momentum $\mid$ of the plate are related as $\mu=\frac{q}{2 m} l$. Solution:...

Consider a nonconducting ring of radius

Question: Consider a nonconducting ring of radius $\mathrm{r}$ and mass $\mathrm{m}$ which has a total charge q distributed uniformly on it. The ring is rotated about its axis with an angular speed $\omega$. (a) Find the equivalent electric current in the ring, (b) find the magnetic moment $\mu$ of the ring. (c) Show that $\mu=\frac{q}{2 m} l$ where $\mid$ is the angular momentum of the ring about its axis of rotation. Solution:...

A square coil of edge I having n turns carries a current i.

Question: A square coil of edge I having n turns carries a current i. It is kept on a smooth horizontal plate. A uniform magnetic field B exists in a directional parallel to an edge. The total mass of the coil is $M$. What should be the minimum value of $B$ for which the coil will start tipping over? Solution:...

A circular loop carrying a current i has wire of total length

Question: A circular loop carrying a current i has wire of total length $\mathrm{L}$. A uniform magnetic field B exists parallel to the plane of the loop. (a) Find the torque on the loop. (b) If the same length of the wire is used to form a square loop, what would be the torque? Which is larger? Solution:...

A circular coil of radius 2.0cm has 500 turns in it and carries a current of 1.0A.

Question: A circular coil of radius $2.0 \mathrm{~cm}$ has 500 turns in it and carries a current of $1.0 \mathrm{~A}$. Its axis makes an angle of $30^{\circ}$ with the uniform magnetic field of magnitude $0.40 T$ that exists in the space. Find the torque acting on the coil. Solution:...

Divide 15 into two parts such that the square of one number multiplied

Question: Divide 15 into two parts such that the square of one number multiplied with the cube of the other number is maximum. Solution:...

A rectangular loop of sides 20cm and 10cm carries a current of 5.0A.

Question: A rectangular loop of sides $20 \mathrm{~cm}$ and $10 \mathrm{~cm}$ carries a current of $5.0 \mathrm{~A}$. A uniform magnetic field of magnitude $0.20 \mathrm{~T}$ exists in parallel to the longer side of the loop. (a) What is the force acting on the loop? (b) What is the torque acting on the loop? Solution:...

A 50-turn circular coil of radius 2.0cm carrying a current of 5.0A

Question: A 50 -turn circular coil of radius $2.0 \mathrm{~cm}$ carrying a current of $5.0 \mathrm{~A}$ is rotated in a magnetic field of strength $0.20 \mathrm{~T}$. (a) What is the maximum torque that acts on the coil? (b) In a particular position of the coil, the torque acting on it is half of this maximum. What is the angle between the magnetic field and the plane of the coil? Solution:...

Question 53 A rectangular coil of 100 turns has length 5cm and width 4cm.

Question: A rectangular coil of 100 turns has length $5 \mathrm{~cm}$ and width $4 \mathrm{~cm}$. It is placed with its plane parallel to a uniform magnetic field and a current of $2 \mathrm{~A}$ is sent through the coil. Find the magnitude of the magnetic field $\mathrm{B}$, if the torque acting on the coil is $0.2 \mathrm{~N}-\mathrm{m}$. Solution:...

An electron is emitted with negligible speed from the speed

Question: An electron is emitted with negligible speed from the speed from the negative plate of a parallel plate capacitor charged to a potential difference $V$. The separation between the plates is $d$ and a magnetic field B exists in the space as shown in figure. Show that the electron will fail to strike upper plate if $d\left(\frac{2 m_{\theta} V}{e B_{0}^{2}}\right)^{\frac{1}{2}}$ Solution:...

A particle having a mass m and charge q is released from

Question: A particle having a mass $m$ and charge $q$ is released from the origin in a region in which electric field and magnetic field are given by $\vec{B}=-B_{0} \vec{j}$ and $\vec{E}=E_{0} \vec{k}$. Find the speed of the particle as a function of its z-coordinate. Solution:...

A proton projected in a magnetic field of

Question: A proton projected in a magnetic field of $0.020 \mathrm{~T}$ travels along a helical path of radius $5.0 \mathrm{~cm}$ and pitch $20 \mathrm{~cm}$. Find the components of the velocity of the proton along and perpendicular to the magnetic field. Take the mass of the proton= $1.6 \times 10^{-27} \mathrm{~kg}$. Solution:...

Find two positive numbers whose sum is 16 and the sum of whose squares is minimum.

Question: Find two positive numbers whose sum is 16 and the sum of whose squares is minimum. Solution:...

A particle having a charge of 0.5mc and a mass of

Question: A particle having a charge of $5.0 \mu \mathrm{C}$ and a mass of $5.0 \times 10^{-12} \mathrm{~kg}$ is projected with a speed of $1.0 \mathrm{~km} / \mathrm{s}$ in a magnetic field of magnitude $5.0 \mathrm{mT}$. The angle between the magnetic field and the velocity is $\sin ^{-1}(0.90)$. Show that the path of the particle will be a helix. Find the diameter of the helix and its pitch. Solution:...

A proton goes undeflected in a crossed electric and magnetic field

Question: A proton goes undeflected in a crossed electric and magnetic field (the fields are perpendicular to each other) at a speed of $2.0 \times 10^{5} \mathrm{~m} / \mathrm{s}$. The velocity is perpendicular to both the fields. When the electric field is switched off, the proton moves along a circle of radius $4.0 \mathrm{~cm}$. Find the magnitudes of the electric and the magnetic fields. Take the mass of proton $=1.6 \times 10^{-27}$ $\mathrm{kg}$. Solution:...

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