A vertical wire is carrying a current in the upward direction. It is placed in a magnetic field pointing towards the east. Find the direction of the force on the wire
Answers
Answer:
The direction of the magnetic force is normally outwards the plane in which the wire is placed.
Explanation:
Assuming, the direction of x, y and z axes directions as follows:
x-axis: Along the horizontal direction, positive towards east and negative towards west.
y-axis: Along the vertical direction, positive towards the upwards direction and negative towards downwards direction.
z-axis: Along the normal to the plane in which the wire is placed, positive along normally outwards direction and negative along normally inwards direction.
\hat i,\ \hat j,\ \hat k
i
^
,
j
^
,
k
^
are the unit vectors along the x, y and z axes directions respectively.
Given:
Direction of current is upwards.
Direction of magnetic field is along east.
Let,
Current flowing in the wire = II
Length element of the wire, \vec l=l\ \hat j
l
=l
j
^
Magnetic field, \vec B = B\ \hat i
B
=B
i
^
Magnetic force on the wire = \vec F
F
We know that the magnetic force on the wire is given by
\begin{lgathered}\vec F = I\vec l \times \vec B\\=Il\hat i\times B\hat j\\=IlB(\hat i\times \hat j)\\=IlB(\hat k)\ \ \ \ \ \ \ \ \ \ \because \hat i\times \hat j=\hat k.\\\end{lgathered}
F
=I
l
×
B
=Il
i
^
×B
j
^
=IlB(
i
^
×
j
^
)
=IlB(
k
^
) ∵
i
^
×
j
^
=
k
^
.
Since, the force is along \hat k
k
^
, i.e., along the positive z axis, the direction of the magnetic force is normally outwards the plane in which the wire is placed.
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