A particle of charge 1.0 10⁻¹⁶ . ^6 C moves through a uniform magnetic field B =B₀( i +4 j ) T . The particle velocity at some instant is v =(2 i +4 j ) ms ⁻¹ and the magnetic force acting on it is 3 10⁻¹⁶ k ~N . The magnitude of B₀ is

Step-by-step solution

Force on a charged particle moving in region of a magnetic field is given by F=q( v B ) ...(i) Here, q=1.0 10⁻¹⁶ C aligned & v =(2 i +4 j ) ms ⁻¹, B =B₀( i +4 j ) T & F =3 10⁻¹⁶ k ~N aligned substituting in eq. (i), we get 3 10⁻¹⁶ k =1 10⁻¹⁶ | array ccc i & j & k 2 & 4 & 0 B₀ & 4 B₀ & 0 array | aligned & 3 k = i (0)- j (0)+ k (8 B₀-4 B₀ ) & 3 k =4 B₀ k or B₀= 3 4 =0.75 ~T aligned