Question

A wire of length l carries current i along the y axis and magnetic field B= b (vector i+vector j +vector k)/root 3 .Now caculate magnetic force acting on the wire​

Answer 1

A wire of length l carries current i along the y axis and magnetic field B= b (vector i+vector j +vector k)/root 3 .Now caculate magnetic force acting on the wire....

A wire of length l carries current i along y-axis . so, position of wire, $\vec{L}=l\hat{j}$

magnetic field $\vec{B}=b\left(\frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\right)$

we know, formula of magnetic force, $\vec{F}=i(\vec{L}\times\vec{B})$

= i [ (l)j × b(i + j + k)/√3 ]

= bil/√3 [ j × (i + j + k)]

= bil/√3 [ j × i + j × j + j × k ]

= bil/√3 [ -k + 0 + i ]

= bil/√3 (i - k)

hence, magnetic force $\vec{F}=\frac{bil}{\sqrt{3}}(\hat{i}-\hat{k})$

Answer 2

Answer:

A wire of length l carries current i along the y axis and magnetic field B= b (vector i+vector j +vector k)/root 3 .Now caculate magnetic force acting on the wire....

A wire of length l carries current i along y-axis . so, position of wire, \vec{L}=l\hat{j}

L

=l

j

^

magnetic field \vec{B}=b(\frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}})

B

=b(

3

i

^

+

j

^

+

k

^

)

we know, formula of magnetic force, \vec{F}=i(\vec{L}\times\vec{B})

F

=i(

L

×

B

)

= i [ (l)j × b(i + j + k)/√3 ]

= bil/√3 [ j × (i + j + k)]

= bil/√3 [ j × i + j × j + j × k ]

= bil/√3 [ -k + 0 + i ]

= bil/√3 (i - k)

hence, magnetic force \vec{F}=\frac{bil}{\sqrt{3}}(\hat{i}-\hat{k})

F

=

3

bil

(

i

^

−

k

^

)