744

You visited us 744 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Using Lenz's Law

The magnetic ...

Question

The magnetic field in a region is given by $\to B = B_{0} (\frac{x}{a})^k$ . A square loop of side $d$ is placed with it's edges on the x and y axis. The loop is moved with a constant velocity $\to v = v_{0}^i$ . The emf induced in the loop is :

B_{0} v_{0} d

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{B_{0} v_{0} d^{2}}{2 a}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{B_{0} v_{0} d^{3}}{a^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{B_{0} v_{0} d^{2}}{a}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{B_{0} v_{0} d^{2}}{a}$
$\to B = B_{o} \frac{x}{a}^K$

$\to V = V_{o} ˆ i = \frac{d x}{d t} ˆ i$

consider a strips at x distance from origin
$d Φ = (d \times d x) (B_{o} \frac{x}{a})$

$Φ = \int_{x}^{d + x} \frac{d B_{o}}{a} x d x$

$Φ = \frac{B_{o} d}{2 a} [(d + x)^{2} - x^{2}]$

$Φ = \frac{B_{o} d}{2 a} [d^{2} + 2 d x]$

emf induced $= \frac{d Φ}{d t} = \frac{B_{o} d}{2 a} \times 2 d \times \frac{d x}{d t}$

$= \frac{B_{o} V_{o} d^{2}}{a}$

Suggest Corrections

Similar questions

Q. The magnetic field in a region is given by

\to B = B_{0} (\frac{x}{a})^k

. A sqaure loop of side

d

is placed with its edges along the

x

and

y

axes. The loop is moved with a constant velocity

\to v = v_{0}^i

. The emf induced in the loop is:

Q. The magnetic field in a region is given by

\to B = B_{0} (1 + \frac{x}{a})^k

. A square loop of edge length

d

is placed with its edge along the

x

- and

y

-axes. The loop is moved with a constant velocity

\to v = v_{0}^i

. The emf induced in the loop is

Q. A magnetic field directed along Z axis varies as

B = B_{0} x / a

, where

B_{0} = 2 t e s l a

and

a = 1 m .

A conducting square loop of side

ℓ = \frac{1}{2} m

is placed with its edges parallel to X and Y axes. If the loop is made to move with a constant velocity

v_{0} = 6 m / s

directed along X axis, the induced emf (in volts) in the loop is :

Q. Magnetic field in a region is given by

\to B = B_{0} x^k

. Two loops each of side of

a

, separated by a distance

d

is placed in this magnetic region in the

x y -

plane with one of its sides on

x

-axis as shown in figure. If

F_{1}

is the force on loop

1

and

F_{2}

be the force on loop

2

, then

Q. A conducting square loop of side

L

and resistance

R

moves in it's plane with a uniform velocity

v

perpendicular to one of it's sides. A magnetic induction

B

, constant in time and space, pointing perpendicular to and into the plane of the loop exists everywhere. The current induced in the loop is

Join BYJU'S Learning Program

The magnetic field in a region is given by →B=B0(xa)^k. A square loop of side d is placed with it's edges on the x and y axis. The loop is moved with a constant velocity →v=v0^i. The emf induced in the loop is :

The correct option is D B0v0d2a→B=Boxa^K→V=Voˆi=dxdtˆiconsider a strips at x distance from origindΦ=(d×dx)(Boxa)Φ=∫d+xxdBoaxdxΦ=Bod2a[(d+x)2−x2]Φ=Bod2a[d2+2dx]emf induced =dΦdt=Bod2a×2d×dxdt=BoVod2a

The magnetic field in a region is given by $\to B = B_{0} (\frac{x}{a})^k$ . A square loop of side $d$ is placed with it's edges on the x and y axis. The loop is moved with a constant velocity $\to v = v_{0}^i$ . The emf induced in the loop is :