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State the Lorenz's force and express it in vector form. Which pair of vectors are always perpendicular to each other? Derive the expression for the force acting on a currentcarrying conductor oflength L in a uniform magnetic field 'B'. |
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Answer» Solution :When a point charge q(moving with a velocityvlocated at rat given time t) in presence of both the electric FIELD E (R ) and magnetic field B (r ) force on charge q due to B and E is `vec(F) = vec(F)_(e) + vec(F)_(m)=q vec E(r)+ vec(V) xx vec(B) (r)]`The force actsin a direction perpendicular to both the velocity and the magnetic field. If `vec(V) and vec(B)` are parallel or antiparallel `vec(V) xx vec(B)` is zero and maximum when V and B are perpendicular. When a current carrying conductor of length . L is placed in uniform magnetic field. Let the number density of charge carrier (electrons) be n and 'A' is the area of cross section so total number of charge carrier in conductor is nAL. For steady current I flowing in conductor each electron suffers drift velocity `V_(d)` in the presence of `vec(B)` the force `Fm = (naL )qV_(d) xx B` Here nqVd is current density (J) and `nqV_(d)//A` is I. HENCE, `F= [nqV_(d)]AL xxB=J Al xxB = Il xx B` L =VECTOR of magnitude L ( the length of the conductor and with a direction of current (I), which is not a vector). |
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