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Byju's Answer

Standard XII

Physics

Electric Field Due to Charge Distributions - Approach

A pair of sta...

Question

A pair of stationary and infinitely long bent wires are placed in the x-y plane as shown in figure. The wires carry a current $I = 10 A$ each as shown. The segments L and M are along X- axis. the segments P and Q are along the Y- axis such that $O S = O R = 0.02 m$ . The magnitude and direction of the magnetic induction at origin O is :

100

W b m^{- 2}

vertically upward

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10^{- 4} W b m^{- 2}

vertically downward

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10^{- 4} W b m^{- 2}

vertically upward

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10^{- 2} W b m^{- 2}

vertically downward

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Solution

The correct option is C $10^{- 4} W b m^{- 2}$ vertically upward
$B = B_{1} + B_{2}$
$= \frac{μ_{0} i_{1}}{4 π r_{1}} + \frac{μ_{0} i_{2}}{4 π r_{2}}$ (wire is semi-infinite)
$= \frac{10^{- 7} \times 10}{0.02} + \frac{10^{- 7} \times 10}{0.02}$
$= 10^{- 4} W b m^{- 2}$

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Similar questions

Q. A pair of stationary and infinitely long bent wires is placed in the x-y plane as shown in figure. Each wire carries current of

10 A

. Segments

L

and

M

are along the x-axis.Segments

P

and

Q

are parallel to the y-axis such that

O S = O R = 0.02 m

. Find the magnitude and direction of the magnetic induction at origin

O

in the form of

x \times 10^{- 4}

. What is x.

Q. A pair of stationary and infinitely long bent wires are placed in the XY plane as shown in the figure. The wires carry currents of

I = 10

amp each as shown in the figure. The segments L and M are along the X-axis such that

O S = O R = 0.02

m. Find the magnitude and direction of the magnetic induction at the origin O.

Q. A pair of stationary and infinitely long bent wires are placed in the

x - y

plane as shown in the figure. The two wires carry currents of

4 A

and

9 A

respectively. If the segments

D

and

A

are along

x

-axis and the segments

C

and

F

are parallel to

y

-axis such that

O B = 2 c m

and

O E = 3 c m

, then the magnitude of the magnetic induction at the origin '

O

' is:

(μ_{0} = 4 π \times 10^{- 7} H m^{- 1})

Q. As shown in the figure, two infinitely long, identical wires are bent by

90

and placed in such a way that the segments

L P

and

Q M

are along the x-axis, while segments

P S

and QN are parallel to the

y - a x i s

. If

O P = O Q = 4 c m

, and the magnitude of the magnetic field at

O

10^{4} T

, and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at

O

will be (

μ 0 = 4 π 10^{7} N A 2

)

Figure shows infinitely long bent wires in the plane of paper and each carrying a current $i$ with $O$ as origin and $X$ and $Y$ axis as shown, co-ordinates of points $P$ & $Q$ are $(2 m, 0)$ and $(6 m, 0)$ respectively. Magnetic induction at $P$ is given by $\frac{α μ_{0} i}{32 π}$ . The value of $α$ is

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The correct option is C 10−4Wbm−2 vertically upwardB=B1+B2=μ0i14πr1+μ0i24πr2 (wire is semi-infinite)=10−7×100.02+10−7×100.02=10−4Wbm−2

The correct option is C $10^{- 4} W b m^{- 2}$ vertically upward
$B = B_{1} + B_{2}$
$= \frac{μ_{0} i_{1}}{4 π r_{1}} + \frac{μ_{0} i_{2}}{4 π r_{2}}$ (wire is semi-infinite)
$= \frac{10^{- 7} \times 10}{0.02} + \frac{10^{- 7} \times 10}{0.02}$
$= 10^{- 4} W b m^{- 2}$