Answer: a) 1.46 T and directed to -x.
Explanation: In order to explain the above problem we have to consider the Lorentz force given by:
F=q*v ⊕ B ; ⊕ is the vector product.
The magnitude of B can be obtained as follow:
B=F/(q*v) where q and v are the charge and velocity of the proton.
B=2.2 *10^-13/(9.4*10^5*1.6*10^-19)=1.46 T
The direction of B is directed to x axis because along this direction the proton experiences zero magnetic force.
Knowing that the magnetic force for the proton is directed to positive z direction and by inspection of the vector product bewteen v ( in +y direction) and B ( in x axis, due to zero line forze), we can conclude that the direction of B is to minus x axis.
The magnitude of the magnetic field is 1.46 x 10²⁶ T.
The magnetic field will point in the positive y - direction.
The magnitude of the magnetic field is calculated as follows;
F = qvB
where;
B = F/qV
B = (2.2 x 10¹³) / (1.6 x 10⁻¹⁹ x 9.4 x 10⁵)
B = 1.46 x 10²⁶ T
The direction of the magnetic field will be perpendicular to the magnetic force and same direction as the positive charge.
Thus, the magnetic field will point in the positive y - direction.
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