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Test Index
KEAM 2019 Physics and Chemistry Paper
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© examsnet.com
Question : 17
Total: 120
Consider a circular loop of radius R on the xy-plane carrying a steady current anticlockwise. The magnetic field at the center of the loop is given by
µ
0
2
R
I
∧
x
µ
0
2
R
I
∧
y
µ
0
2
R
I
∧
z
µ
0
R
I
∧
x
µ
0
R
I
∧
y
Validate
Solution:
A circular loop of radius
R
and current
I
is shown in the figure below
From Biot-savart law, the magnetic field at some point in space at distance
R
is given as,
d
B
=
µ
0
4
π
i
d
l
×
P
R
3
Since, the loop is circular in shape so,
=
2
π
R
Now integrating the field in whole length of wire loop
⇒
B
∫
0
d
B
=
µ
0
4
π
i
R
R
3
2
π
R
∫
0
d
l
⇒
B
=
µ
0
4
π
i
R
2
2
π
R
=
µ
0
i
2
R
Also, with help of right hand thumb rule, we can conclude, that the magnetic field is in
+
z
direction.
⇒
B
=
µ
0
i
2
R
⋀
z
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