A straight wire has 8 A current in the -y-direction. The magnetic field is produced due to the current in the wire in addition to this a uniform magnetic field B₀ with magnitude 1.5e-6 T is in the +x-direction.a) In the xz plane, find the magnitude of the magnetic field at the point x = 0 , z = 1.00 mb) Give its direction.c) In the xz plane, find the magnitude of the magnetic field at the point x = 1.00 m , z = 0d) Give its direction.e) In the xz plane, find the magnitude of the magnetic field at the point x = 0 , z = − 0.25 m

Question

A straight wire has 8 A current in the -y-direction. The magnetic field is produced due to the current in the wire in addition to this a uniform magnetic field B₀ with magnitude 1.5e-6 T is in the +x-direction.a) In the xz plane, find the magnitude of the magnetic field at the point   x  =  0  ,     z  =  1.00     mb) Give its direction.c) In the xz plane, find the magnitude of the magnetic field at the point   x  =  1.00     m  ,     z  =  0d) Give its direction.e) In the xz plane, find the magnitude of the magnetic field at the point   x  =  0  ,     z  =  −  0.25     m

meexeniexia17h · Accepted Answer

Step 1Given data:The current in the wire is,   I  =  8     AThe magnetic field in x direction is,       B          0        =  1.5  ×      10          −      6        TPart (a)The point in xz plane is given as   x  =  0     m     and     z  =  1.00     mThe distance of point from origin can be calculated as,  r  =      (    0         m          )              2              +    (    1.00         m          )              2                =      (    1.00         m          )              2                =  1.0     mThe magnetic field acting on point is,      B          p        =                    μ                  0                    I              2      π      r      Substitute the known values,      B          p        =            (      4      π      ×              10                  −          7                    T      ×              m        A            )      (      8             A      )              2      π      (      1.0             m      )          =  1.6  ×      10          −      6        TThe total magnetic field acting on the point is,  B  =      B          0        −      B          p      Substitute the known values,  B  =  1.5  ×      10          −      6        T  −  1.6  ×      10          −      6        T    =  −  0.1  ×      10          −      6        T    =  −  1  ×      10          −      7        TThus, the magnitude of total magnetic field acting on the point is   1  ×      10          −      7        TStep 2Part (b)The negative sign of total magnetic field in part (b) indicates that the magnetic field will be directed in negative x-direction.Part (c)The point in xz plane is given as   x  =  1.00     m     and     z  =  0     mThe distance of point from origin can be calculated as,  r  =      (    1.00         m          )              2              +    (    0         m          )              2                =      (    1.00         m          )              2                =  1.0     mThe magnetic field acting on point is,      B          p        =                    μ                  0                    I              2      π      r      Substitute the known values,      B          p        =            (      4      π      ×              10                  −          7                    T      ×              m        A            )      (      8             A      )              2      π      (      1.0             m      )        =  1.6  ×      10          −      6        TThe total magnetic field acting on the point is,  B  =            B              0                    2              +          B              p                    2            Substitute the known values,  B  =      (    1.5    ×          10              −        6              T          )              2              +    (    1.6    ×          10              −        6              T          )              2                =      2.25    ×          10              −        12                    T              2              +    2.56    ×          10              −        12                    T              2                =      4.81    ×          10              −        12              T      ≈  2.19  ×      10          −      6        TThus, the magnitude of total magnetic field acting on the point is   2.19  ×      10          −      6        TStep 3Part (d)The direction of the magnetic field can be given as,  tan  ⁡  θ  =            B              0                    B              p            Substitute the known values,  tan  ⁡  θ  =            1.5      ×              10                  −          6                    T              1.6      ×              10                  −          6                    T          θ  =      tan          −      1        ⁡  (  0.9375  )    ≈      43.1          ∘      Thus, the direction of magnetic field is       43.1          ∘      Part (e)The point in xz plane is given as   x  =  0     m     a  n  d     z  =  −  0.25     mThe distance of point from origin can be calculated as,  r  =      (    0         m          )              2              +    (    −    0.25         m          )              2                =      (    0.25         m          )              2                =  0.25     mThe magnetic field acting on point is,      B          p        =            (      4      π      ×              10                  −          7                    T      ×              m        A            )      (      8             A      )              2      π      (      0.25             m      )          =  6.4  ×      10          −      6        TThe total magnetic field acting on the point is,  B  =      B          0        +      B          p      Substitute the known values,  B  =  1.5  ×      10          −      6        T  +  6.4  ×      10          −      6        T    =  7.9  ×      10          −      6        TThus, the magnitude of total magnetic field acting on the point is  7.9  ×      10          −      6        T

A straight wire has 8 A current in the -y-direction. The magnetic field is produced due to the current in the wire in addition to this a uniform magnetic field B₀ with magnitude 1.5e-6 T is in the +x-direction.

Answered question

Answer & Explanation

New Questions in Electromagnetism