Single Choice

When a proton is released from rest in room, it starts with an initial acceleration $${ a }_{ 0 }$$ towards west When it is projected towards north with a speed $${ V }_{ 0 }$$ it moves with an initial acceleration $${ 3a }_{ 0 }$$ towards west. The electric and magnetic fields in the room are :

A$$\dfrac { { ma }_{ 0 } }{ e } east,\dfrac { { 3ma }_{ 0 } }{ { ev }_{ 0 } } down$$
B$$\dfrac { { ma }_{ 0 } }{ e } west,\dfrac { { 3ma }_{ 0 } }{ { ev }_{ 0 } } up$$
C$$\dfrac { { ma }_{ 0 } }{ e } west,\dfrac { { 2ma }_{ 0 } }{ { ev }_{ 0 } } down$$
Correct Answer
D$$\dfrac { { ma }_{ 0 } }{ e } east,\dfrac { { 3ma }_{ 0 } }{ { ev }_{ 0 } } up$$

Solution

Initial acceleration $$={ a }_{ 0 }$$
when a proton is released from rest in a room it starts with an initial acceleration $${ a }_{ 0 }$$ towards west.
$${ F }_{ 1 }=$$ electric force acting on the proton in west direction
$$q=$$ charge on proton
$$E=$$ electric field in the region in west direction
$$m=$$ mass of proton
electric force on the proton can be given on $${ F }_{ 1 }=qE$$
Using Newton's second law
$${ F }_{ 1 }={ ma }_{ 0 }$$
hence,
$${ ma }_{ 0 }=qE$$
$$E={ ma }_{ 0 }/q$$ Along west
Case -2
$${ V }_{ 0 }=$$ initial velocity of the particle
$${ F }_{ 2 }=$$ magnetic force acting on the proton in west direction electric force on proton $$=3{ ma }_{ 0 }$$
$${ F }_{ 1 }+{ F }_{ 2 }=3{ ma }_{ 0 }$$
$${ ma }_{ 0 }+{ F }_{ 2 }=3{ ma }_{ 0 }$$
maximum magnetic force is given by
$${ F }_{ 2 }=q{ V }_{ 0 }B$$
So, $$q{ V }_{ 0 }B=2{ ma }_{ 0 }$$
$$B=2{ ma }_{ 0 }/q{ V }_{ 0 }$$ (down).
Option C

SIMILAR QUESTIONS

Magnetism

A particle having a mass of $$10^{-2}$$ kg carries a charge of $$5 \times 10^{-8}$$ C. The particle is given an initial horizontal velocity of $$10^5 ms^{-1}$$ in the presence of electric field $$\overset{\rightarrow}{E}$$ and magnetic field $$\overset{\rightarrow}{B}$$. To keep the particle moving in a horizontal direction, it is necessary that (i) $$\overset{\rightarrow}{B}$$ should be perpendicular to the direction of velocity and $$\overset{\rightarrow}{E}$$ should be along the direction of velocity. (ii) Both $$\overset{\rightarrow}{B}$$ and $$\overset{\rightarrow}{E}$$ should be along the direction of velocity. (iii) Both $$\overset{\rightarrow}{B}$$ and $$\overset{\rightarrow}{E}$$ are mutually perpendicular and perpendicular to the direction of velocity. (iv) $$\overset{\rightarrow}{B}$$ should be along the direction of velocity and $$\overset{\rightarrow}{E}$$ should be perpendicular to the direction of velocity. Which one of the following pairs of statements is possible

Magnetism

When a proton is released from the rest in a room, it starts with an initial acceleration $$a_{0}$$ towards north with a speed $$v_{0}$$ it moves with an initial acceleration $$3a_{0}$$ towards west. The electric and magnetic fields in the room are

Magnetism

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields $$\overrightarrow{E} = E_{0}\hat{j}$$ and $$\overrightarrow{B} = B_{0}\hat{j}$$. At time t = 0, this charge has velocity $$\overrightarrow{v}$$ in the x-y plane, making an angle $$\theta$$ with the x axis. Which of the following option(s) is(are) correct for time t > 0 ?

Magnetism

A closed coil having $$100$$ turns is rotated in a uniform magnetic field $$B=4.0\times { 10 }^{ -4 }T$$ about a diameter whcih is perpendicular to the field. The angular velocity of rotation is $$300$$ revolutions per minute. The area of the coil is $$25{cm}^{2}$$ and its resistance is $$4.0\Omega$$. Find (a) the average emf developed in half turn from a position where the coil is perpendicular to the magnetic field, (b) the average emf in a full turn and (c) the net charge displaced in part (a)

Magnetism

A charged particle moves in a gravity-free space without change in velocity. Which of the following is/are possible?

Magnetism

A charged particle moves along a circle under the action of possible constant electric and magnetic fields. Which of the following are possible?

Magnetism

A charged particle goes undeflected in a region containing electric and magnetic fields. It is possible that

Magnetism

If a charged particle goes unaccelerated in a region containing electric and magnetic fields,

Magnetism

Let $$\vec E$$ and $$\vec B$$ denote electric and magnetic fields in a frame S and $$\vec E'$$ and $$\vec B'$$ in another frame S' moving with respect to S at a velocity $$\vec v$$. Two of the following equations are wrong. Identify them:

Magnetism

If a charged particle at rest experiences no electromagnetic force,

Contact Details