Question

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 ​

Answer 1

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.
• $\hat i,\ \hat j,\ \hat k$ 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 = $I$
• Length element of the wire, $\vec l=l\ \hat j$
• Magnetic field, $\vec B = B\ \hat i$
• Magnetic force on the wire = $\vec F$

We know that the magnetic force on the wire is given by

$\vec F = I\vec l \times \vec B\\=Il\hat i\times B\hat j\\=IlB(\hat i\times \hat j)\\=IlB(\hat k)\ \ \ \ \ \ \ \ \ \ \because \hat i\times \hat j=\hat k.$

Since, the force is along $\hat k$, i.e., along the positive z axis, the direction of the magnetic force is normally outwards the plane in which the wire is placed.

Answer 2

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.

are the unit vectors along the x, y and z axes directions respectively.