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Byju's Answer
Standard XII
Physics
Towards Biot-Savart Law
The magnetic ...
Question
The magnetic field at the origin due to a current element
i
.
→
d
l
placed at a position
→
r
is
A
μ
0
i
4
π
→
d
l
×
→
r
r
3
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B
μ
0
i
4
π
→
r
×
→
d
l
r
3
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C
−
μ
0
i
4
π
→
r
×
→
d
l
r
3
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D
−
μ
0
i
4
π
→
d
l
×
→
r
r
3
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Solution
The correct options are
B
−
μ
0
i
4
π
→
r
×
→
d
l
r
3
C
μ
0
i
4
π
→
d
l
×
→
r
r
3
B
=
μ
0
4
π
i
→
d
l
×
→
r
r
3
=
−
μ
0
4
π
i
→
r
×
→
d
l
r
3
since
→
d
l
×
→
r
=
−
(
→
r
×
→
d
l
)
Options (A) and (C) are correct
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0
Similar questions
Q.
What is the magnetic field
→
d
B
at a distance
→
r
due to a small current element
→
d
l
carrying current I?
Q.
What is the magnetic field
→
d
B
at a distance
→
r
due to a small current element
→
d
l
carrying current I?
Q.
The magnetic field at the origin due to a current element
i
d
l
→
placed at a position
r
→
is
(a)
μ
0
i
4
π
d
l
→
×
r
→
r
3
(b)
-
μ
0
i
4
π
r
→
×
d
l
→
r
3
(c)
μ
0
i
4
π
r
→
×
d
l
→
r
3
(d)
-
μ
0
i
4
π
d
l
→
×
r
→
r
3
Q.
Let
→
a
,
→
b
and
→
c
be three non-coplanar vectors and let
→
p
,
→
q
and
→
r
be the vectors defined by
→
p
=
→
b
×
→
c
[
→
a
→
b
→
c
]
,
→
q
=
→
c
×
→
a
[
→
a
→
b
→
c
]
,
→
r
=
→
a
×
→
b
[
→
a
→
b
→
c
]
. Then
(
→
a
+
→
b
)
⋅
→
p
+
(
→
b
+
→
c
)
⋅
→
q
+
(
→
c
+
→
a
)
⋅
→
r
=
Q.
If expressions for the magnetic field at a point due to a current element, in C.G.S.system is given by
d
→
B
=
μ
0
4
π
i
(
d
−
−−
→
l
×
→
r
)
a
∗
r
3
. Find a.
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