New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Magnetics question

2024 · 29 Jan · Shift 2 · Q89

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Physics
Magnetics
2024 · 29 Jan · Shift 2 · Q89

Magnetics question

2024 · 29 Jan · Shift 2 · Q89

JEE MainPhysicsMagneticsNumerical+4 / −1

A charge of

4.0 \mu \mathrm{C}

is moving with a velocity of

4.0 \times 10^6 \mathrm{~ms}^{-1}

along the positive

y

axis under a magnetic field

\vec{B}

of strength

(2 \hat{k}) \mathrm{T}

. The force acting on the charge is

x \hat{i} N

. The value of

x

is

\underline{\hspace{2cm}}

.

Numerical answer

View written solutionFree

Correct answer: 32

Given data

Charge: $q = 4.0\,\mu\text{C} = 4.0 \times 10^{-6}\,\text{C}$
Velocity: $\vec v = 4.0 \times 10^6 \, \hat{j}\,\text{m s}^{-1}$
Magnetic field: $\vec B = 2\hat{k}\,\text{T}$

We need the magnetic force:

\vec F = q(\vec v \times \vec B)

Find the cross product

\vec v \times \vec B = (4.0 \times 10^6\hat{j}) \times (2\hat{k})

Taking constants out:

\vec v \times \vec B = 8.0 \times 10^6 (\hat{j} \times \hat{k})

Using unit vector relation:

\hat{j} \times \hat{k} = \hat{i}

So,

\vec v \times \vec B = 8.0 \times 10^6 \hat{i}

Multiply by charge

\vec F = q(\vec v \times \vec B)

\vec F = (4.0 \times 10^{-6})(8.0 \times 10^6)\hat{i}

\vec F = 32\hat{i}\,\text{N}

Compare with the given form

Given that the force is $x\hat{i}\,\text{N}$ , we get

x = 32

Comparison with stored correct answer

Stored correct answer = $32$

This matches the derived answer.

More from Magnetics

Two insulated circular loop A and B of radius ' $a$ ' carrying a current of ' $I$ ' in the anti clockwise direction as shown in the figure. The magnitude of the magnetic induction at the centre will be : Includes diagram2024 · MCQ
The current of $1 m$ flows in a square loop of sides $X 2 \times 1 0^{- 7} T$ is placed in air. The magnetic field at the centre of the loop is $X 2 \times 1 0^{- 7} T$ . The value of $X$ is .2024 · Numerical
A rigid wire consists of a semicircular portion of radius $R$ and two straight sections. The wire is partially immerged in a perpendicular magnetic field $B = B_{0} \hat{k}$ as shown in figure. The magnetic force on the wire if it has a… Includes diagram2024 · MCQ
An electron moves through a uniform magnetic field $B = B_{0} \hat{i} + 2 B_{0} \hat{j} T$ . At a particular instant of time, the velocity of electron is $u = 3 \hat{i} + 5 \hat{j} m / s$ . If the magnetic force acting…2024 · Numerical
A uniform magnetic field of $2 \times 1 0^{- 3} T$ acts along positive $Y$ -direction. A rectangular loop of sides $10 cm$ and $5 A$ with current of $Y - Z$ is in $Y - Z$ plane. The current is in…2024 · MCQ
Two circular coils $P$ and $Q$ of 100 turns each have same radius of $P$ . The currents in $P$ and $R$ are $1 A$ and $2 A$ respectively. $P$ and $Q$ are placed with their planes mutually perpendicular with their centers…2024 · Numerical
Find the magnetic field at the point $P$ in figure. The curved portion is a semicircle connected to two long straight wires. Includes diagram2023 · MCQ
A charge particle of $2 μ C$ accelerated by a potential difference of $4 mT$ enters a region of uniform magnetic field of magnitude $4 mT$ at right angle to the direction of field. The charge particle…2023 · Numerical